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Hamming Code

Hamming code

In telecommunication, a Hamming code is an error-correcting code named after its inventor, Richard Hamming. Hamming codes can detect single and double-bit errors, and correct single-bit errors as well. In contrast, the simple parity code cannot detect errors where two bits are transposed, nor can it help correct the errors it can find.

History

Hamming worked at Bell Labs in the 1940s on the Bell Model V computer, an electromechanical relay-based monster with cycle times in seconds. Input was fed in on punch cards, which would invariably have read errors. During weekdays, special code would find errors and flash lights so the operators could correct the problem. During after-hours periods and on weekends, when there were no operators, the machine simply moved on to the next job. Hamming worked on weekends, and grew increasingly frustrated with having to restart his programs from scratch due to the unreliability of the card reader. Over the next few years he worked on the problem of error-correction, developing an increasingly powerful array of algorithms. In 1950 he published what is now known as Hamming Code, which remains in use in some applications today.

Codes predating Hamming

A number of simple error-detecting codes were used before Hamming codes, but none were nearly as effective as Hamming codes in the same overhead of space.

Parity

Parity adds a single bit that indicates whether the number of 1 bits in the preceding data was even or odd. If a single bit is changed in transmission, the message will change parity and the error can be detected at this point. (Note that the bit that changed may have been the parity bit itself!) The most common convention is that a parity value of 1 indicates that there is an odd number of ones in the data, and a parity value of 0 indicates that there is an even number of ones in the data. Parity checking is not very robust, since if the number of bits changed is even, the check bit will be valid and the error will not be detected. Moreover, parity does not indicate which bit contained the error, even when it can detect it. The data must be discarded entirely, and re-transmitted from scratch. On a noisy transmission medium a successful transmission could take a long time, or even never occur. Parity does have the advantage, however, that it is about the best possible code that uses only a single bit of space.

Two-out-of-five code

In the 1940s Bell used a slightly more sophisticated code known as the two-out-of-five code. This code ensured that every block of five bits (known as a 5-block) had exactly two 1s. The computer could tell if there was an error if in its input there were not exactly two 1s in each block. Two-of-five was still only able to detect single bits; if one bit flipped to a 1 and another to a 0 in the same block, the two-of-five rule remained true and the error would go undiscovered.

Repetition

Another code in use at the time repeated every data bit several times in order to ensure that it got through. For instance, if the data bit to be sent was a 1, an n=3 repetition code would send "111". If the three bits received were not identical, an error occurred. If the channel is clean enough, most of the time only one bit will change in each triple. Therefore, 001, 010, and 100 each correspond to a 0 bit, while 110, 101, and 011 correspond to a 1 bit, as though the bits counted as "votes" towards what the original bit was. A code with this ability to reconstruct the original message in the presence of errors is known as an error-correcting code. Such codes cannot correctly repair all errors, however. In our example, if the channel flipped two bits and the receiver got "001", the system would detect the error, but conclude that the original bit was 0, which is incorrect. If we increase the number of times we duplicate each bit to four, we can detect all two-bit errors but can't correct them (the votes "tie"); at five, we can correct all two-bit errors, but not detect all three-bit errors. Moreover, the repetition code is extremely inefficient, reducing throughput by three times in our original case, and the efficiency drops drastically as we increase the number of times each bit is duplicated in order to detect and correct more errors.

Hamming codes

If more error-correcting bits are included with a message, and if those bits can be arranged such that different incorrect bits produce different error results, then bad bits could be identified. In a 7-bit message, there are seven possible single bit errors, so three error control bits could potentially specify not only that an error occurred but also which bit caused the error. Hamming studied the existing coding schemes, including two-of-five, and generalized their concepts. To start with he developed a nomenclature to describe the system, including the number of data bits and error-correction bits in a block. For instance, parity includes a single bit for any data word, so assuming ASCII words with 7-bits, Hamming described this as an (8,7) code, with eight bits in total, of which 7 are data. The repetition example would be (3,1), following the same logic. The information rate is the second number divided by the first, for our repetition example, 1/3. Hamming also noticed the problems with flipping two or more bits, and described this as the "distance" (it is now called the Hamming distance, after him). Parity has a distance of 2, as any two bit flips will be invisible. The (3,1) repetition has a distance of 3, as three bits need to be flipped in the same triple to obtain another code word. A (4,1) repetition (each bit is repeated four times) has a distance of 4, so flipping two bits in the same group will no longer go undiscovered. Hamming was interested in two problems at once; increasing the distance as much as possible, while at the same time increasing the information rate as much as possible. During the 1940s he developed several encoding schemes that were dramatic improvements on existing codes. Key to all of his systems was to have the parity bits overlap, such that they managed to check each other as well as the data. The algorithm for use of parity bits for the general 'Hamming code' is simple: #All bit positions that are powers of two are used as parity bits. (positions 1, 2, 4, 8, 16, 32, 64, etc.) #All other bit positions are for the data to be encoded. (positions 3, 5, 6, 7, 9, 10, 11, 12, 13, 14, 15, 17, etc.) #Each parity bit calculates the parity for some of the bits in the code word. The position of the parity bit determines the sequence of bits that it alternately checks and skips. #
- Position 1(n=1): check 0 bit(n-1) ,skip 1 bit(n), check 1 bit(n), skip 1 bit(n), check 1 bit(n), etc. #
- Position 2(n=2): check 1 bit(n-1), skip 2 bits(n), check 2 bits(n), skip 2 bits(n), check 2 bits(n), etc. #
- Position 4(n=4): check 3 bits(n-1), skip 4 bits(n), check 4 bits(n), skip 4 bits(n), check 4 bits(n), etc. #
- Position 8(n=8): check 7 bits(n-1), skip 8 bits(n), check 8 bits(n), skip 8 bits(n), check 8 bits(n), etc. #
- Position 16(n=16): check 15 bits(n-1), skip 16 bits(n), check 16 bits(n), skip 16 bits(n), check 16 bits(n), etc. #
- Position 32(n=32): check 31 bits(n-1), skip 32 bits(n), check 32 bits(n), skip 32 bits(n), check 32 bits(n), etc. #
- And so on.

Example using the (11,7) Hamming code

Consider the 7-bit data word "0110101". To demonstrate how Hamming codes are calculated and used to detect an error, see the tables below. They use d to signify data bits and p to signify parity bits. Firstly the data bits are inserted into their appropriate positions and the parity bits calculated in each case using even parity. : The new data word (with parity bits) is now "10001100101". We now assume the final bit gets corrupted and turned from 1 to 0. Our new data word is "10001100100"; and this time when we analyse how the Hamming codes were created we flag each parity bit as 1 when the even parity check fails. : The final step is to evaluate the value of the parity bits (remembering the lowest value bit goes furthest to the right). The integer value of the parity bits is 11, signifying that the 11th bit in the data word (including parity bits) is wrong and needs to be flipped. : Flipping the 11th bit gives changes 10001100100 back into 10001100101. Removing the Hamming codes gives the original data word of 0110101. Note that as parity bits do not check each other, if a single parity bit check fails and all others succeed, then it is the parity bit in question that is wrong and not any bit it checks. Finally, suppose two bits change, at positions x and y. If x and y have the same bit at the 2^k position in their binary representations, then the parity bit corresponding to that position checks them both, and so will remain the same. However, some parity bit must be altered, because x ≠ y, and so some two corresponding bits differ in x and y. Thus, the Hamming code detects all two bit errors — however, it cannot distinguish them from 1-bit errors.

Hamming code (7,4)

Today, Hamming code really refers to a specific (7,4) code Hamming introduced in 1950. Hamming Code adds three additional check bits to every four data bits of the message. Hamming's (7,4) algorithm can correct any single-bit error, or detect all single-bit and two-bit errors. Since the medium would have to be uselessly noisy for 2 out of 7 bits to be lost, Hamming's (7,4) is effectively lossless.

Example of the use of matrices over GF(2)

Hamming codes work through extending the idea of parity by multiplying matrices called Hamming matrices. For the Hamming (7,4) code, we use two closely related matrices, call them :

H_e := \begin
1 & 0 & 0 & 0 \\
0 & 1 & 0 & 0 \\
0 & 0 & 1 & 0 \\
0 & 0 & 0 & 1 \\
1 & 1 & 0 & 1 \\
1 & 0 & 1 & 1 \\
0 & 1 & 1 & 1 \\
\end

and :

H_d := \begin
0 & 0 & 0 & 1 & 1 & 1 & 1 \\
0 & 1 & 1 & 0 & 0 & 1 & 1 \\
1 & 0 & 1 & 0 & 1 & 0 & 1 \\
\end

We use a block of four payload data bits (hence the 4 in the name), and accrue another three redundant data bits (hence the 7 in the name as 4+3=7). To send the data, we consider the block of data bits we wish to send as a vector, for example, for "1011", the vector is :

\mathbf=\begin 1 \\ 0 \\ 1 \\ 1 \end

Suppose we want to send this data. We take the product of

H_e

and p, with entries modulo 2: :

H_e\mathbf = \begin
1 & 0 & 0 & 0 \\
0 & 1 & 0 & 0 \\
0 & 0 & 1 & 0 \\
0 & 0 & 0 & 1 \\
1 & 1 & 0 & 1 \\
1 & 0 & 1 & 1 \\
0 & 1 & 1 & 1 \\
\end\begin 1 \\ 0 \\ 1 \\ 1 \end=
\begin 1 \\ 0 \\ 1 \\ 1 \\ 0 \\ 1 \\ 0 \end=\mathbf

The receiver will multiply

H_d

and r, to see if an error has occurred. Performing this multiplication (again, entries modulo 2): :

H_d\mathbf = \begin
0 & 0 & 0 & 1 & 1 & 1 & 1 \\
0 & 1 & 1 & 0 & 0 & 1 & 1 \\
1 & 0 & 1 & 0 & 1 & 0 & 1 \\
\end\begin 1 \\ 0 \\ 1 \\ 1 \\ 0 \\ 1 \\ 0 \end = \begin 0 \\ 0 \\ 0 \end

As we have the zero vector, the receiver can conclude that no error has occurred. Suppose that now a single bit error has occurred. Mathematically, we can write :

\mathbf+\mathbf_i

modulo 2, where e_i is the ith unit vector, that is, a zero vector with a 1 in the ith place, counting from 1. Thus the above expression signifies a single bit error in the ith place. Now, if we multiply this vector by

H_d

: :

H_d(\mathbf+\mathbf_i) = H_d\mathbf + H_d\mathbf_i

As r is the received data without error, the product of

H_d

and r is zero. Thus :

H_d\mathbf + H_d\mathbf_i = \mathbf + H_d\mathbf_i = H_d\mathbf_i

Now, the product of

H_d

with the ith standard basis vector picks out that column of

H_d

, we know the error occurs in the place where this column of

H_d

occurs. As we have constructed

H_d

in a particular way, we can interpret this column as a binary number -- for example, (1, 0, 1) is a column of

H_d

and thus corresponds to the 5th place, and thus know where the error has occurred and can correct it. For example, suppose we have :

\mathbf = \mathbf+\mathbf_2 = \begin 1 \\ 1 \\ 1 \\ 1 \\ 0 \\ 1 \\ 0 \end

Now, :

H_d\mathbf = \begin
0 & 0 & 0 & 1 & 1 & 1 & 1 \\
0 & 1 & 1 & 0 & 0 & 1 & 1 \\
1 & 0 & 1 & 0 & 1 & 0 & 1 \\
\end\begin 1 \\ 1 \\ 1 \\ 1 \\ 0 \\ 1 \\ 0 \end = \begin 0 \\ 1 \\ 0 \end

which corresponds to the second column ("010" in binary is 2 in decimal), and thus an error occurs in the second place, and thus can be corrected. It is not difficult to show that only single bit errors can be corrected using this scheme. Alternatively, Hamming codes can be used to detect single and double bit errors, by merely noting that the product of

H_d

is nonzero whenever errors have occurred. However, Hamming codes cannot do both.

Hamming codes with additional parity

Hamming codes can be used together with an extra parity bit, to allow for the detection of two-bit errors, without preventing single-bit errors from being corrected. Alternatively, single-bit, two-bit and three-bit errors can be detected, but this then prevents the correction of single-bit errors. The extra parity bit applies to all bits after the Hamming code check bits have been added. When using correction, if a parity error is detected and the Hamming code indicates that there is an error, this error can be corrected. However, if a parity error is not detected but the Hamming code indicates that there is an error, this is assumed to have been due two-bit error, which is detected but cannot be corrected.

External links

- [http://www.ee.unb.ca/cgi-bin/tervo/hamming.pl CGI script for calculating Hamming distances (from R. Tervo, UNB, Canada)] Category:Error detection and correction ja:ハミング符号 ko:%ED%95%B4%EB%B0%8D_%EB%B6%80%ED%98%B8

Telecommunication

Telecommunication refers to communication over long distances. In practice, something of the message may be lost in the process. Telecommunication covers all forms of distance and/or conversion of the original communications, including radio, telegraphy, television, telephony, data communication and computer networking. The elements of a telecommunication system are a transmitter, a medium (line) and possibly a channel imposed upon the medium (see baseband and broadband as well as multiplexing), and a receiver. The transmitter is a device that transforms or encodes the message into a physical phenomenon; the signal. The transmission medium, by its physical nature, is likely to modify or degrade the signal on its path from the transmitter to the receiver. The receiver has a decoding mechanism capable of recovering the message within certain limits of signal degradation. Sometimes, the final "receiver" is the human eye and/or ear (or in some extreme cases other sensory organs) and the recovery of the message is done by the brain (see psychoacoustics.) Telecommunication can be point-to-point, point-to-multipoint or broadcasting, which is a particular form of point-to-multipoint that goes only from the transmitter to the receivers. One of the roles of the telecommunications engineer is to analyse the physical properties of the line or transmission medium, and the statistical properties of the message in order to design the most effective encoding and decoding mechanisms. When systems are designed to communicate through human sensory organs (mainly those for vision and hearing), physiological and psychological characteristics of human perception must be taken into account. This has important economic implications and engineers must research what defects can be tolerated in the signal and not significantly degrade the viewing or hearing experience.

Examples of human (tele)communications

In a simplistic example, consider a normal conversation between two people. The message is the sentence that the speaker decides to communicate to the listener. The transmitter is the language areas in the brain, the motor cortex, the vocal cords, the larynx, and the mouth that produce those sounds called speech. The signal is the sound waves (pressure fluctuations in air particles) that can be identified as speech. The channel is the air carrying those sound waves, and all the acoustic properties of the surrounding space: echoes, ambient noise, reverberation. Between the speaker and the listener, there might be other devices that do or do not introduce their own distortions of the original vocal signal (for example a telephone, a HAM radio, an IP phone, etc.) The receiver is the listener's ear and auditory system, the auditory nerve, and the language areas in the listener's brain that will "decode" the signal into meaningful information and filter out background noise. All channels have noise. Another important aspect of the channel is called the bandwidth. A low bandwidth channel, such as a telephone, cannot carry all of the audio information that is transmitted in normal conversation, causing distortion and irregularities in the speaker's voice, as compared to normal, in-person speech.

External links

- [http://web.archive.org/web/20040413074912/www.ericsson.com/support/telecom/index.shtml Ericsson's Understanding Telecommunications] at archive.org (Ericsson removed the book from their site in Sep 2005)
- [http://www.carrieraccessbilling.com/telecommunications-glossary-a.asp Intec Telecom Systems' Telecom Dictionary]
- [http://www.mobile-phone-directory.org/Glossary/ Mobile Phone Directory Telecommunications Glossary]
- [http://www.tiaonline.org Telecommunications Industry Association (TIA)]
- [http://www.aronsson.se/hist.html Aronsson's Telecom History Timeline]
- [http://www.alcatel.com/atr Alcatel Telecommunications Review] Telecom magazine published since 1922
- [http://www.teleclick.ca Telecommunications Industry News]
- [http://www.bt.com BT] British Telecommunications company
- Category:Digital Revolution ms:Telekomunikasi ja:電気通信 th:โทรคมนาคม

Richard Hamming

Richard Wesley Hamming (February 11, 1915 – January 7, 1998) was a mathematician whose work had many implications for computer science and telecommunications. His contributions to science include the Hamming code (which makes use of a Hamming matrix), the Hamming window (described in section 5.8 of Digital Filters), Hamming numbers, Sphere-packing or hamming bound and the Hamming distance. He was born in Chicago, Illinois and died in Monterey, California. He received his bachelor's degree from the University of Chicago in 1937, a master's degree from the University of Nebraska in 1939, and finally a Ph.D. from the University of Illinois at Urbana-Champaign in 1942. He was a professor at the University of Louisville when World War II was going on, and left to work on the Manhattan Project in 1945, programming one of the earliest electronic digital computers to calculate the solution to equations provided by the project's physicists. The objective of the program was to discover if the detonation of an atomic bomb would ignite the atmosphere. The result of the computation was that this would not occur, and so the United States used the bomb, first in a test in New Mexico, and then twice against Japan. Later 1946-1976 he worked at the Bell Telephone Laboratories, where he collaborated with Claude E. Shannon. On July 23 1976 he moved to the Naval Postgraduate School, where he worked as an Adjunct Professor until 1997, when he became Professor Emeritus. He was a founder of the Association for Computing Machinery, which he also served as its President. __NOTOC__

Awards and professional recognition

- Association for Computing Machinery Turing Award, 1968.
- Fellow of the IEEE, 1968.
- IEEE Emanuel R. Piore Award, 1979.
- Member of the National Academy of Engineering, 1980.
- University of Pennsylvania Harold Pender Award, 1981.
- IEEE Richard W. Hamming Medal, 1988.
- Eduard Rhein Award, 1996. The Richard W. Hamming Medal is an award given annually by IEEE for 'exceptional contributions to information sciences, systems and technology'.

Books

- Numerical Methods for Scientists and Engineers, McGraw-Hill, 1962; second edition 1973.
- Calculus and the Computer Revolution, Houghton-Mifflin, 1968.
- Introduction To Applied Numerical Analysis, McGraw-Hill, 1971.
- Computers and Society, McGraw-Hill, 1972.
- Digital Filters, Prentice-Hall, 1977; second edition 1983; third edition 1989. ISBN 048665088X
- Coding and Information Theory, Prentice-Hall 1980; second edition 1986.
- Methods of Mathematics Applied to Calculus, Probability, and Statistics, Prentice-Hall, 1985.
- The Art of Probability for Scientists and Engineers, Addison-Wesley, 1991.
- Art of Doing Science and Engineering: Learning to Learn, Gordon and Breach, 1997.

Quotes

- "Machines should work. People should think."
- "Does anyone believe that the difference between the Lebesgue and Riemann integrals can have physical significance, and that whether say, an airplane would or would not fly could depend on this difference? If such were claimed, I should not care to fly in that plane."
- "There are wavelengths that people cannot see, there are sounds that people cannot hear, and maybe computers have thoughts that people cannot think."
- "The purpose of computing is insight, not numbers."
- "Newton said, 'If I have seen further than others, it is because I've stood on the shoulders of giants. These days we stand on each other's feet!'" ([http://www.cs.virginia.edu/~robins/YouAndYourResearch.html You and Your Research])
External links and references

- FOLDOC: [http://wombat.doc.ic.ac.uk/foldoc/foldoc.cgi?Richard+Hamming Richard Hamming (bio)]
- Richard Hamming, [http://www.cs.virginia.edu/~robins/YouAndYourResearch.html You and Your Research] Hamming, Richard Hamming, Richard Hamming, Richard Hamming, Richard Hamming, Richard ko:%EB%A6%AC%EC%B2%98%EB%93%9C_%ED%95%B4%EB%B0%8D

Bell Labs

Bell Telephone Laboratories (or sometimes AT&T Bell Laboratories), best known as Bell Labs, was originally the research and development arm of the United States Bell System. It was the premier corporate facility of its type, developing a range of revolutionary technologies from telephone switches to specialized coverings for telephone cables, including the famous discovery of the transistor.

History

In 1925, Walter Gifford, then president of AT&T, established Bell Telephone Laboratories Inc as a separate entity which took over work previously conducted by the research division of Western Electric's engineering department. Half of Bell Labs was owned by Western Electric, the other half being owned by AT&T. Discoveries made at Bell Labs include:
- 1925: Facsimile (fax) transmission first demonstrated publicly
- 1927: Long-distance television transmission, of images of Herbert Hoover, from Washington to New York
- 1928: Thermal noise in a resistor is measured by J.B. Johnson; Harry Nyquist provides a theoretical analysis.
- 1920s: The one-time pad cipher invented by Gilbert Vernam and Joseph Mauborgne; Bell's Claude Shannon later proved that it was unbreakable
- 1933: Foundation of radio astronomy laid by Karl Jansky; in his work investigating the origins of static on long distance communications, he discovered that radio waves were being emitted from the centre of the galaxy
- 1933: Stereo signals transmitted live from Philadelphia to Washington D.C.
- 1937: The vocoder, the first electronic speech synthesizer, invented and demonstrated by Homer Dudley
- 1940: The photovoltaic cell developed by Russell Ohl
- 1947: The transistor is invented by John Bardeen, William Bradford Shockley, and Walter Houser Brattain, all of whom subsequently won the Nobel Prize in Physics in 1956
- 1948: "A Mathematical Theory of Communication", one of the founding works in information theory, published by Claude Shannon in the Bell System Technical Journal; it built in part on earlier work in the field by Bell researchers Harry Nyquist and Ralph Hartley
- 1949: First remote operation of a teleprinter, controlled in New Hampshire by a computer at Bell Labs in New York City
- 1956: TAT-1, the first transatlantic telephone cable laid between Scotland and Newfoundland
- 1957: MUSIC, one of the first computer programs to play electronic music, created by Max Mathews; New greedy algorithms developed by Robert C. Prim and Joseph Kruskal, revolutionizing network design as we know it
- 1958: The laser is first described in a technical paper by Arthur Schawlow and Charles Townes
- 1962: Light-emitting diodes (LEDs) invented by Nick Holonyak
- 1964: Carbon dioxide laser invented by Kumar Patel
- 1965: Penzias and Wilson discovered the Cosmic Microwave Background (Nobel Prize 1978)
- 1966: Orthogonal frequency-division multiplexing (OFDM), a key technology in wireless services, developed and patented by R. W. Chang
- 1968: Molecular beam epitaxy developed by J.R. Arthur and A.Y. Cho; allows semiconductor chips and laser matrices to be created one atomic layer at a time
- 1969: UNIX operating system is created by Dennis Ritchie and Ken Thompson
- 1970: C programming language developed by Ritchie and Thompson
- 1971: A computerized switching system for telephone traffic, invented by Erna Schneider Hoover, receives one of the first software patents
- 1976: Fiber optics systems first tested in Georgia
- 1980: First single-chip 32-bit microprocessor, the BELLMAC-32A, is demonstrated; it goes into production in 1982
- 1980: TDMA and CDMA digital cellular telephone technology patented
- 1982: Fractional quantum Hall effect discovered by Horst Störmer and former Bell Labs researchers Robert B. Laughlin and Daniel C. Tsui; they won a Nobel Prize for it in 1998
- 1983: The C++ programming language is developed by Bjarne Stroustrup
- 1984: Karmarkar Linear Programming Algorithm developed by mathematician Narendra Karmarkar
- 1985: Laser cooling used to slow and manipulate atoms by Steven Chu and team
- 1980s: Plan 9 operating system is devloped as a replacement for Unix
- 1980s: A Radiodrum, a three dimensional electronic instrument is developped
- 1988: TAT-8 is the first fiber optic transatlantic cable
- 1990: WaveLAN is the first wireless local area network (LAN)
- 1991: 56K modem technology patented by Nuri Dagdeviren and team
- 1994: Quantum cascade laser invented by Federico Capasso, Claire Gmachl and team
- 1995: Wireless internet access first demonstrated
- 1996: SCALPEL electron lithography, which prints features atoms wide on microchips, invented by Lloyd Harriott and team
- 1996: The Inferno operating system, an update of Plan 9, is created by Dennis Ritchie and team using the new concurrent Limbo programming language
- 1997: Smallest practical transistor created, 60 nanometers or 182 atoms wide
- 1998: First optical router
- 1998: First combination of voice and data traffic on an Internet Protocol (IP) network
- 2000: DNA machine prototypes developed
- 2000: Progressive geometry compression algorithm makes widespread 3-D communication practical
- 2000: First electrically powered organic laser
- 2000: Large-scale map of cosmic dark matter provided
- 2000: F-15, an organic material that makes plastic transistors possible, invented After the 1984 divestiture agreement with the government that broke up AT&T, Bellcore was split off from Bell Labs to provide the same R&D functions for the newly created local exchange carriers. AT&T was also limited to using the Bell trademark in association with Bell Labs. In 1996 AT&T spun off Bell Labs, along with most of its equipment-manufacturing business, into a new company named Lucent Technologies. AT&T retained a smaller number of researchers to form AT&T Laboratories. In 2002 Jan Hendrik Schön, a German physicist, was fired from Bell Labs after his work was found to contain fraudulent data; it was the first case of fraud in the lab's history. Over a dozen of Schön's papers were found to contain fictional or altered data, including a paper on molecular-scale transistors that was portrayed as a breakthrough. At its height, Bell Labs had research and development facilities all over the USA,though mostly concentrated in the majority of areas in New Jersey; but before the telecomm bust of 2000, the Naperville-Lisle location had the single largest concentration of people (about 11,000). Among the locations were Westminster in Colorado, Crawford Hill, Freehold, Holmdel, Lincroft, Long Branch, Middletown, Murray Hill, Piscataway, Red Bank, Whippany, Naperville, Lisle,Columbus in Ohio, Allentown and Breinigsville. Bell Labs is currently located in Murray Hill, New Jersey. Within the past five years, many of the former Bell Labs locations have been scaled back or shutdown entirely.

Basis

The work done by Bell Labs was broadly divided into three categories: research, systems engineering, and development. Research created the theoretical underpinnings for telecommunications. It covered subjects such as mathematics, physics, material sciences, behavioral sciences, and computer programming theory. Systems engineering concerned itself with conceiving the highly complex systems that make up the telecommunication networks. Development, by far the largest of Bell Labs' activities designed the specific systems -- both hardware and software -- needed to build the Bell System's telecommunications networks.

Calculators built by Bell Labs

- Model I - Complex Number Calculator, completed January 1940, for doing calculations of complex numbers
- Model II - Relay Calculator or Relay Interpolator, September 1943, for aiming anti-aircraft guns by interpolating from positions
- Model III - Ballistic Computer, June 1944, for calculations of ballistic trajectories
- Model IV - Bell Laboratories Relay Calculator, March 1945, a second Ballistic Computer
- Model V - Bell Laboratories General Purpose Relay Calculator, two were built: July 1946 and February 1947. These were general-purpose programmable computers using electromechanical relays.
- Model VI - November 1950, an enhanced Model V.

External links

- [http://www.bell-labs.com/ Bell Labs]
- [http://www.bell-labs.com/about/history/timeline.html Timeline of discoveries]
- [http://www.bell-labs.com/org/1133/Research/Acoustics/AnechoicChamber.html Bell Labs' Murray Hill anechoic chamber]
- [http://maps.google.com/maps?ll=40.683404,-74.400744&spn=0.004066,0.006605&t=k&hl=en Google maps satellite view of the Murray Hill Facility] Category:Bell System Category:Telecommunications history ko:벨 연구소 ja:ベル研究所

Electromechanical

In engineering, electromechanics combines the sciences of electromagnetism of electrical engineering and mechanics. Mechatronics is the discipline of engineering that combines mechanics, electronics and information technology. Electromechanical devices are those that combine electrical and mechanical parts. These include electric motors and mechanical devices powered by them, such as calculators and adding machines; switches, solenoids, relays, crossbar switches and stepping switches. Early on, "repeaters" originated with telegraphy and were electromechanical devices used to regenerate telegraph signals. The telephony crossbar switch is an electromechanical device for switching telephone calls. They were first widely installed in the 1950s in both the United States and England, and from there quickly spread to the rest of the world. They replaced most earlier designs like the Strowger switch in larger installations. Nikola Tesla, one of the great engineers, pioneered the field of electromechanics. Paul Nipkow proposed and patented the first electromechanical television system in 1885. Electrical typewriters developed, up to the 1980s, as "power-assisted typewriters." They contained a single electrical component in them, the motor. Where the keystroke had previously moved a typebar directly, now it engaged mechanical linkages that directed mechanical power from the motor into the typebar. This was also true of the forthcoming IBM Selectric. At Bell Labs, in the 1940s, the Bell Model V computer was developed. It was an electromechanical relay-based monster with cycle times in seconds. In 1968 Garrett Systems were invited to produce a digital computer to compete with electromechanical systems then under development for the main flight control computer in the US Navy's new F-14 Tomcat fighter. Today, though, common items which would have used electromechanical devices for control, today use, less expensive and more effectively, a standard integrated circuit (containing a few million transistors) and write a computer program to carry out the same task through logic. Transistors have replaced almost all electromechanical devices, are used in most simple feedback control systems, and appear in huge numbers in everything from traffic lights to washing machines.

Punch card

The punch card (or "Hollerith" card) is a recording medium for holding information for use by automated data processing machines. Made of thin cardboard, the punch card represents information by the presence or absence of holes in predefined positions on the card. In the first generation of computing, from the 1920s into the 1950s, punch cards were the primary medium for data storage and processing. Eventually, during the late 1970's to early 1980's, the punch card was phased out as a medium for storage of computer data and replaced by huge floppy disks. Today, punch cards are long obsolete outside of a few legacy systems and specialized applications. legacy systems

Origins

legacy systems The punched card predates computers considerably. As early as 1725 Basile Bouchon used perforated paper loop in a loom to establish the pattern to be reproduced on cloth, and in 1726 his co-worker Jean-Baptiste Falcon improved on his design by using perforated paper cards attached to one another, which made it easier to change the program quickly. The Bouchon-Falcon loom was semi-automatic and required manual feed of the program. Joseph Jacquard used punched cards in 1801 as a control device for the more automatic Jacquard looms, which met with great success. Charles Babbage, who originated the idea of a programmable computer, adopted Jacquard's system of punched cards to control the sequence of computations in the design for his analytical engine in 1837 [http://www.cs.uiowa.edu/~jones/cards/history.html]. Such cards were used as an input method for the primitive calculating machines of the late 19th century. The version by Herman Hollerith, patented on June 8, 1887 and used with mechanical tabulating machines in the 1890 U.S. Census, was a piece of cardboard about 90 mm by 215 mm, with round holes. This was the same size as the dollar bill of the time, so that storage cabinets designed for money could be used for his cards. The early applications of punched cards all used specifically-designed card layouts. It wasn't until around 1928 that punched cards and machines were made "general purpose". In that year, punched cards were made a standard size, exactly 7-3/8 inch by 3-1/4 inch (187.325 by 82.55 mm), reportedly corresponding to the US currency of the day, though some sources characterise this assertion as urban legend. To compensate for the cyclical nature of the Census Bureau's demand for his machines, Hollerith founded the Tabulating Machine Company (1896) which was one of three companies that merged to form IBM in 1911. The IBM 80-column punching format, with rectangular holes, eventually won out over the UNIVAC 90-character format, which used 45 columns (2 characters in each) of 12 round holes. IBM (Hollerith) punched cards are made of smooth stock, .007 of an inch thick. There are about 143 cards to the inch thickness; a group of such cards is called a deck. Punch cards were widely known as just IBM cards.

Functional details

UNIVAC The method is quite simple: On a piece of light-weight cardboard, successive positions either have a hole punched through them or are left intact. The rectangular bits of paper punched out are called chads. Thus, each punch location on the card represents a single binary digit (or "bit"). Each column on the card contained several punch positions (multiple bits).

IBM punch card format

The IBM card format, which became standard, held 80 columns of 12 punch locations each, representing 80 characters. Originally only numeric information was coded with 1 or 2 punchs per column: digits (digit[0-9]) and signs (zone[12,11] – sometimes overpunching the Least Significant Digit). Later, codes were introduced for upper-case letters and special characters. A column with 2 punches (zone[12,11,0] + digit[1-9]) was a letter; 3 punches (zone[12,11,0] + digit[2-4] + 8) was a special character. The introduction of EBCDIC in 1964 allowed columns with as many as 6 punches (zones[12,11,0,8,9] + digit[1-7]). The punch cards were 7 and 3/8 inches long by 3 and 1/4 inches high and were 0.007 inch thick with one of the upper corners cut at an angle.

Corner cut

A major reason for the corner cut was so the punch card could not be inserted backwards or upside down. If the punch card was inserted backwards or upside down it hit a small plastic pin in the machine called the corner cut pin. This would engage a micro switch and halt the machine operation until the card was inserted properly with the corner cut on the correct side of the punch card as used in that system. Stopping the machine meant the machine would not continue to sort or validate. Many computer installations used cards with the opposite corner cut (sometimes no corner cut) as "job separators", so that an operator could stack several job decks in the card reader at the same time and be able to quickly separate the decks manually when he removed them from the stacker. These cards were prepunched (e.g., a JCL command to start a new job) in large quantities in advance. This was especially useful when the main computer did not read the cards directly, but instead read their images from magnetic tape that was prepared offline by card to tape converters or smaller computers. card to tape converter

Key punches

Data was entered on a machine called a keypunch, which was like a large, very noisy typewriter. Often the text was also printed at the top of the card, allowing humans to read the text as well. This was done using a machine called an interpreter. Later model keypunches could do this as well. Multi-character data, such as words or large numbers, was stored in adjacent card columns known as fields. For applications in which accuracy was critical, the practice was to have two different operators key the same data, with the second using a card-verifier instead of a card-punch. Verified cards would be marked with a rounded notch on the right end. Failed cards would be replaced by a key punch operator. There was a great demand for key-punch operators, usually women, who worked full-time on key punch and verifier machines. Electromechanical equipment (called unit record equipment) for punching, sorting, tabulating and printing the cards was manufactured. These machines allowed sophisticated data processing tasks to be accomplished long before computers were invented. The card readers used an electrical (metal brush) or, later, optical sensor to detect which positions on the card contained a hole. They had high-speed mechanical feeders to process around one hundred cards per minute. All processing was done with electromechanical counters and relays. The machines were programmed using wire patch panels.

Other formats

unit record equipment Other coding schemes, sizes of card, and hole shapes were tried at various times. Mark sense cards had printed ovals that humans would fill in with a pencil. Specialized card punches could detect these marks and punch the corresponding information into the card. There were also needle cards with all the punch positions perforated so data could be punched out manually, one hole at a time, with a device like a blunt pin with its wire bent into a finger-ring on the other end. In the early 1970s, IBM introduced a new, smaller, round-hole, 96-column card format along with the IBM System 3 computer. Aperture cards are a specialized use of punch cards for storing "blueprints". A drawing is photographed onto 35 mm film and the image is mounted in a window on the right half of the punch card. Information about the drawing, e.g. the drawing number, is punched in the left half. IBM punch cards could be used with early computers in a binary mode where every column (or row) was treated as a simple bitfield, and every combination of holes was permitted . In this binary mode, cards could be made in which every possible punch position had a hole: these were called "lace cards." For example, the IBM 700/7000 series scientific computers treated every row as two 36-bit words, usually in columns 1-72, ignoring the last 8 columns (but this was programable using a plugboard in the card reader and punch to select the 72 columns used). Other computers, like the IBM 1130, used every possible hole.

Advantages

In its earliest uses, the punch card was not just a data recording medium, but a controlling element of the data processing operation. Electrical pulses produced when the read brushes passed through holes punched in the cards directly triggered electro-mechanical counters, relays, and solenoids. Cards were inexpensive and provided a permanent record of each transaction. Large organizations had warehouses filled with punch card records. One reason punch cards persisted into the early computer age was that an expensive computer was not required to encode information onto the cards. When the time came to transfer punch card information into the computer, the process could occur at very high speed, either by the computer itself or by a separate, smaller computer (e.g. an IBM 1401) that read the cards and wrote the data onto magnetic tapes or, later, on removable hard disks, that could then be mounted on the larger computer, thus making best use of expensive mainframe computer time.

Obsolescence

Punched-card systems fell out of favor in the mid to late 1970s, as disk storage became cost effective, and affordable interactive terminals meant that users could edit their work with the computer directly rather than requiring the intermediate step of the punched cards. However, their influence lives on through many standard conventions and file formats. The terminals that replaced the punched cards displayed 80 columns of text, for compatibility with existing software. Many programs still operate on the convention of 80 text columns, although strict adherence to that is fading as newer systems employ graphical user interfaces with variable-width type fonts.

Dimpled and hanging chads

The term for the punched card area which is removed during a punch is chad. One notorious problem with a punched card system of tabulation is the incomplete punch; this can lead to a smaller hole than expected, or to a mere slit on the card, or to a mere dimple on the card. Thus a chad which is still attached to the card is a hanging chad. This technical problem was claimed by the Democratic Party to have influenced the 2000 U.S. presidential election in the state of Florida; critics claimed that voting machines which used punched cards to tabulate votes generated improperly rendered records of several hundred votes, spread out over an entire state, which allegedly tipped the vote in favor of George W. Bush over Al Gore.

External links

- [http://www.cs.uiowa.edu/~jones/cards/ Doug Jones' Punch Card history site] (Collection shows examples of left, right, and no corner cuts.)
- [http://homepages.cwi.nl/~dik/english/codes/80col.html Various punched card codes]
- [http://www.wired.com/wired/archive/7.03/punchcards_pr.html The Undead - Wired magazine article about modern day use of punch cards]
- [http://groups.msn.com/scottfisher/misc.msnw?action=ShowPhoto&PhotoID=201 Scott Fishers Pennsylvania turnpike Ticket, (IBM Punch card w square holes) toll ticket webpage 1970's]
- [http://www.fourmilab.ch/documents/univac/cards.html UNIVAC Punch Card Gallery] (Shows examples of both left and right corner cuts.) In part, Category:Computer storage media Category:History of computing ja:パンチカード

Nomenclature

Nomenclature is a system of naming and categorizing objects in a given category. Linnaeus popularized one of the best-known examples: he used binary names (e.g. in two parts, a process known as binomial nomenclature) to name species of minerals, vegetables, and animals. The names he coined for the last two categories were the start of present day botanical and zoological nomenclature, codified in the ICBN and ICZN. Other codes are also derived from these. The combination of a genus name and a species descriptor serves to uniquely label each species of organism. For example, humankind is uniquely named by the name Homo sapiens. No other species of animal can have this name. In this way, every species is given a specific identifier that is accepted worldwide, transcending common names that are often neither unique nor consistent from place to place and language to language.

Hamming distance

In information theory, the Hamming distance, named after Richard Hamming, is the number of positions in two strings of equal length for which the corresponding elements are different. Put another way, it measures the number of substitutions required to change one into the other. For example:
- The Hamming distance between 1011101 and 1001001 is 2.
- The Hamming distance between 2143896 and 2233796 is 3.
- The Hamming distance between "toned" and "roses" is 3. The Hamming weight of a string is its Hamming distance from the zero string (string consisting of all zeros) of the same length. That is, it is the number of elements in the string which are not zero: for a binary string this is just the number of 1's, so for instance the Hamming weight of 11101 is 4. The Hamming distance between two words a and b, viewed as elements of a vector space, can then be seen as the Hamming weight of a-b. If a and b are binary strings this is equivalent to a+b and to a XOR b. The Hamming distance is also equivalent to the Manhattan distance between two vertices in an n-dimensional hypercube, where n is the length of the words. The Hamming distance is used in telecommunication to count the number of flipped bits in a fixed-length binary word, an estimate of error, and so is sometimes called the signal distance. Hamming weight analysis of bits is used in several disciplines including information theory, coding theory, and cryptography. For comparing strings of different lengths, or strings where insertions or deletions are expected, not just substitutions, a more sophisticated metric like the Levenshtein distance is more appropriate. Adapted in part from Federal Standard 1037C.

References

Richard W. Hamming. Error-detecting and error-correcting codes, Bell System Technical Journal 29(2):147-160, 1950.

1950

1950 (MCML) was a common year starting on Sunday (link will take you to calendar).

Events

January

- January 5 - U.S. Senator Estes Kefauver introduces a resolution calling for examination of organized crime in the U.S.
- January 6 - The United Kingdom recognizes the People's Republic of China. The Republic of China severs diplomatic relations with Britain in response.
- January 9 - The Israeli government recognizes the People's Republic of China.
- January 11 - Huk guerillas attack the town of Hermosa in Bataan, Philippines.
- January 12 - Huk guerillas attack the town of Tuyn, kill two and torch the city of Staingnacan.
- January 12 - British submarine Truculent collides with a Swedish oil tanker in River Thames - 64 dead.
- January 13 - Finland forms diplomatic relations to People's Republic of China
- January 15 - Volcanic cloud kills 5000 in Mount Lamington, New Guinea
- January 17 - The Great Brinks Robbery - 11 thieves steal more than $2 million from an armored car in Boston, Massachusetts
- January 21 - Alger Hiss is convicted of perjury
- January 23 - The Knesset passes a resolution that states Jerusalem is the capital of Israel.
- January 24 - Cold War: Klaus Fuchs confesses his wartime espionage at Los Alamos to British interrogators - formally charged February 2
- January 26 - India promulgates its constitution forming a republic and Rajendra Prasad is sworn in as its first president.
- January 28 - Somaliland is put under Italian mandate
- January 29 - Lord Balfour criticizes the fact that rationing is still in force in Britain
- January 31 - President Harry S. Truman announces a program to develop the hydrogen bomb
- January 31 - Last Kuomintang troops surrender in continental China

February

- February 1 - Chiang Kai-shek re-elected as a president of the Republic of China
- February 4 - Ingrid Bergman's illegitimate child arouses ire in USA
- February 9 - Red scare: In his speech to the Republican Women's Club at the McClure Hotel in Wheeling, West Virginia, Senator Joseph McCarthy accuses the United States Department of State of being filled with 205 Communists.
- February 11 - Two Vietcong battalions attack a French base in Indochina
- February 11 - Finland recognizes Indonesia
- February 12 - Pro-communist riots in Paris
- February 12 - European Broadcasting Union founded
- February 13 - In USA army begins to deploy anti-aircraft cannons to protect nuclear stations and military targets
- February 14 - The Soviet Union and the People's Republic of China sign a mutual defense treaty
- February 15 - Juho Kusti Paasikivi re-elected president of Finland
- February 19 - Konrad Adenauer tries unsuccessfully to negotiate with East Germany to begin unification.
- February 12 - Albert Einstein warns that nuclear war could lead to mutual destruction
- February - British Labour Party forms a new government.

March-April

- March 1 - 7.25 PM West South Baptist Church(negro) in Bestridge, Nebraska blows up - all the choir is late for rehearsals
- March 1 - Klaus Fuchs is convicted of spying for the Soviet Union by giving them top secret atomic bomb data.
- March 1 - Acting Chinese President Li Tsung-jen ends his term in office
- March 1 - Chiang Kai-shek resumes his duties as Chinese president after moving his government to Taipei, Taiwan
- March 3 - Poland states that it intends to exile all Germans.
- March 8 - The Soviet Union claims to have an atomic bomb.
- March 12-March 13 - In Belgium, the referendum over the monarchy shows 57.7% support the return of king Léopold III, 42.3% against.
- March 14 - Ship Cygnet hits mine off the Dutch coast.
- March 17 - University of California, Berkeley researchers announce the creation of element 98 which they have named "californium".
- March 20 - Government of Poland decides to confiscate the property of Polish church
- March 22 - Egypt demands that Britain remove all its troops in Suez Canal
- April 15 - King Léopold III of Belgium announces that he is ready to abdicate in favor of his son Baudouin
- April 24 - Jordan formally annexes West Bank
- April 27 - Apartheid: In South Africa, the Group Areas Act is passed formally segregating races.
- April 27 - Britain formally recognizes Israel

May-June

- May 6 - Tollund Man found
- May 9 - Robert Schuman presents his proposal on the creation of an organized Europe, indispensable to the maintenance of peaceful relations. This proposal, known as the "Schuman declaration", is considered to be the beginning of the creation of what is now the European Union.
- May 11 - Kefauver Committee hearings about US organized crime begin
- May 25 - Brooklyn-Battery Tunnel is formally opened to traffic
- May 29 - St. Roch, first ship to circumnavigate North America arrives in Halifax Nova Scotia.
- June 3 - First ascent of Annapurna I, 10th highest mountain in the world.
- June 6 - Turkey: The Adhan in Arabic is legalized
- June 8 - Sir Thomas Blamey becomes the only Field Marshal in Australian history.
- June 10 - French police capture escaped murderer Emile Buisson in Paris restaurant
- June 24 - 58 persons were killed when a commercial airliner crashed into Lake Michigan. The reason for the disaster is unknown. Only fragments of the plane and the bodies of passengers were ever found.
- June 25 - Beginning of Korean War. In the USA, people began to hoard supplies in case of rationing and shortages.
- June 25 - NSC-68 enacted by President Truman, setting US foreign policy for the next twenty years.
- June 28 - Korean War - North Korean forces capture Seoul
- June 29 - United States defeats England 1-0 in the . For more details, see England v United States (1950).

July

- July 5 - Sicilian bandit leader Salvatore Giuliano killed in a shootout with carabinieri
- July 5 - Korean War: Task Force Smith - First clash between American and North Korean forces.
- July 5 - Zionism: The Knesset passes the Law of Return which grants all Jews the right to immigrate to Israel.
- July 6 - East Germany agrees with Poland on the Oder-Neisse line - West Germany does not at this time
- July 16 - Uruguay beat Brazil 2-1 to win 1950 World Cup
- July 17 - Julius and Ethel Rosenberg arrested
- July 19 - 15 SS-men sentenced to death in East Germany
- July 20 - Tydings committee report to US senate denounces Joe McCarthy - he begins a public attack on members of the committee standing for election in 1950
- July 20 - In Belgium, the United Chambers adopt a decree which reinstates King Léopold III in his royal dignity.
- July 23 - King Léopold III of Belgium returns to Brussels
- July 24 - Hoax by J. Bam Morrison begins the tradition of "Sucker Day" in Wetumka, Oklahoma
- July 25 - Walter Ulbricht elected the general secretary of the communist party of East Germany
- July 28 - In Belgium, demonstrations and strikes break out as a result of King Léopold III's return. In Liège, three labourers are shot.

August-September

- August 5 - Florence Chadwick swims over English Channel in 13 hours, 22 minutes
- August 5 - A bomb-laden B-29 Superfortress crashes into a residential area in California. 17 dead, 68 injured.
- August 6 - Riot in Brussels in monarchist demonstrations
- August 8 - Winston Churchill supports idea of pan-European army allied with Canada and USA
- August 15 - Earthquake and floods in Assam, India - 574 deaths, 5,000,000 believed homeless
- September 1 - Hungarian major general Laszlo Viragen defects to Austria and applies for political asylum
- September 4 - Beetle Bailey comic strip started.
- September 7 - Coal mine collapses in New Cumnock, Scotland - 13 miners dead. 116 rescued.
- September 7 - The gameshow Truth or Consequences debuts on television.
- September 12 - Communist riots in Berlin
- September 13 - First main-line diesel-electric locomtives run in Australia
- September 15 - Allied troops land in Inchon, occupied by North Korea, to begin the Battle of Inchon.
- September 19 - West Germany decides to fire all its communist officials
- September 26 - Indonesia admitted to the United Nations

October

- October 1 - The comic strip Peanuts by Charles M. Schulz is first published in seven US newspapers.
- October 3 - Getúlio Dornelles Vargas, elected president of Brazil, for a five-year term.
- October 5 - Indonesian government quells riots in the Moluccas
- October 11 - The Federal Communications Commission issues the first license to broadcast television in color, to CBS (RCA will successfully dispute and block the license from taking effect, however).
- October 15 - In East Germany, communists win 99.7% of the vote
- October 20 - Australia passes the Communist Party Dissolution Act, later struck down by the High Court.
- October - Sister Mary Teresa begins her charity work in Calcutta and becomes known as Mother Teresa

November

- November 1 - Pope Pius XII defines a new dogma of Roman Catholicism: that God assumed Mary's body into Heaven after her death.
- November 1 - Puerto Rican nationalists Griselio Torresola and Oscar Collazo attempt to assassinate US President Harry S. Truman, who is staying at the Blair-Lee House in Washington, D.C. during White House repairs.
- November 4 - United Nations ends the diplomatic isolation of Spain
- November 8 - Korean War: While in an F-80, United States Air Force Lt. Russell J. Brown intercepts two North Korean MiG-15s near the Yalu River and shots them down in the first jet-to-jet dogfight in history.
- November 11 - The Mattachine Society founded in Los Angeles as the first Gay liberation organization
- November 13 - Colonel Carlos Delgado Chalbaud is kidnapped and murdered in Caracas.
- November 18 - United Nations accepts the formation of Libyan national council
- November 20 - T. S. Eliot speaks against television in the UK
- November 22 - Anti-British riots in Egypt
- November 22 - Shirley Temple announces her retirement from show business
- November 23 - George Robb was born in Aylth, Scotland
- November 26 - Korean War: Troops from the People's Republic of China move into North Korea and launch a massive counterattack against South Korean and American forces, ending any thought of a quick end to the conflict.
- November 28 - Greece and Yugoslavia reform diplomatic relations
- November 29 - Korean War: North Korean and Chinese troops force a desperate retreat of United Nations forces from North Korea.
- November 30 - Truman threatens to use nuclear weapons in Korea

December

- December 3 - Etna volcano erupts in Sicily
- December 12 - Paula Ackerman becomes the first woman in the United States to serve a congregation as a Rabbi, a few weeks after the death of her husband.
- December 24-December 25 - Scottish nationalists take the Stone of Scone from Westminster Abbey
- December 28 - The Peak District becomes Britain's first National Park.

Unknown date

- Ralph Schneider founds Diners Club - it initially only works in 27 restaurants in New York City.
- United Nations building finished.
- First pagers developed.
- Antihistamine discovered.
- First TV remote control, Zenith Radio's Lazy Bones is marketed.
- IBM Israel begins operating in Tel Aviv
- Japanese soldier Yuichi Akitsu surrenders in the Philippines
- President Harry Truman sends United States military personnel to Vietnam to aid French forces.
- National Council of the Churches of Christ in the USA founded.

Births

January-February

- January 12 - Sheila Jackson Lee, American politician
- January 16 - Debbie Allen, American actress, dancer, and choreographer
- January 18 - Gilles Villeneuve, Canadian race car driver
- January 21 - Billy Ocean, West Indian-born musician
- January 23 - Richard Dean Anderson, American actor
- January 24 - Benjamin Urrutia, Ecuadoran author and scholar
- January 29 - Jody Scheckter, South African race car driver
- February 3 - Morgan Fairchild, American actress
- February 4 - Pamela Franklin, British actress
- February 6 - Natalie Cole, American singer
- February 10 - Mark Spitz, American swimmer
- February 12 - Michael Ironside, American actor
- February 13 - Peter Gabriel, British musician
- February 16 - Peter Hain, British politician
- February 18 - John Hughes, American film director, producer, and writer
- February 20 - Ken Shimura, Japanese television performer and actor
- February 22 - Julius Erving, American basketball player
- February 22 - Julie Walters, English actress
- February 22 - Miou-Miou, French actress
- February 22 - Ellen Greene, American actress
- February 25 - Neil Jordan, Irish film director, writer, and producer
- February 25 - Néstor Kirchner, President of Argentina
- February 26 - Helen Clark, Prime Minister of New Zealand

March-April

- March 2 - Karen Carpenter, American singer and drummer (d. 1983)
- March 4 - Rick Perry, Governor of Texas
- March 9 - Doug Ault, baseball player (d. 2004)
- March 9 - Danny Sullivan, American race car driver
- March 11 - Bobby McFerrin, American singer
- March 11 - Jerry Zucker, American film producer, director, and writer
- March 13 - William H. Macy, American actor
- March 18 - Brad Dourif, American actor
- March 20 - William Hurt, American actor
- March 26 - Teddy Pendergrass, American singer
- March 29 - Bud Cort, American actor
- March 30 - Robbie Coltrane, British actor and comedian
- April 3 - Sally Thomsett, British actress
- April 4 - Christine Lahti, American actress
- April 5 - Agnetha Fältskog, Swedish singer and songwriter (ABBA)
- April 10 - Ken Griffey, Sr., baseball player
- April 12 - Kari Palaste, Finnish architect
- April 22 - Peter Frampton, English musician
- April 25 - Lenora Branch Fulani, American Presidential candidate
- April 28 - Jay Leno, American comedian and talk show host
- April 29 - Paul Holmes , a radio and television broadcaster in New Zealand

May-September

- May 1 - Danny McGrain, Scottish footballer
- May 1 - Dann Florek, American actor
- May 3 - Howard Ashman, American lyricist (d. 1991)
- May 7 - Randall 'Tex' Cobb, American boxer and actor
- May 12 - Bruce Boxleitner, American actor
- May 12 - Gabriel Byrne, Irish actor
- May 13 - Stevie Wonder, American singer and musician
- May 16 - Johannes Georg Bednorz, German physicist, Nobel Prize laureate
- May 17 - Janez Drnovšek, Slovene politician
- May 17 - Valeria Novodvorskaya, Russian politician and dissident
- May 18 - Thomas Gottschalk, German television host
- May 18 - Rodney Milburn, American athlete (d. 1997)
- May 18 - Mark Mothersbaugh, American composer and musician (Devo)
- May 22 - Bernie Taupin, English songwriter
- May 22 - Mary Tamm, British actress
- June 1 - Tom Robinson, English singer and musician
- June 3 - Suzi Quatro, American singer and actress
- June 6 - John Byrne, American comic book creator
- July 18 - Sir Richard Branson, British entrepreneur
- July 18 - Glenn Hughes, American vocalist (d. 2001)
- July 19 - Per-Kristian Foss, Norwegian Minister of Finance
- August 11 - Gennidy Nikonov, Russian weapon designer
- August 14 - Bob Backlund, American professional wrestler
- August 15 - Anne, Princess Royal of England
- August 16 - Hasely Crawford, West Indian athlete
- August 27 - Charles Fleischer, American actor
- September 2 - Rosanna DeSoto, American actress
- September 14 - Paul Kossoff, British guitarist (Free) (d. 1976)
- September 17 - Narendra Modi, chief minister of Gujarat
- September 21 - Charles Clarke, British politician
- September 21 - Bill Murray, American actor and comedian
- September 28 - John Sayles director and screenwriter

October-December

- October 1 - Randy Quaid, American actor
- October 5 - Jeff Conaway, American actor
- October 9 - Jody Williams, American teacher and aid worker, recipient of the Nobel Peace Prize
- October 12 - Kaga Takeshi, Japanese actor
- October 22 - Bill Owens, Governor of Colorado
- October 28 - Sihem Bensedrine, Tunisian human rights activist
- October 31 - John Candy, American comedian and actor
- October 31 - Jane Pauley, American television broadcaster and journalist
- November 1 -

Hamming code

History

Codes predating Hamming

Parity

Two-out-of-five code

Repetition

Hamming codes

Example using the (11,7) Hamming code

Hamming code (7,4)

Example of the use of matrices over GF(2)

Hamming codes with additional parity

See also

External links

Telecommunication

Examples of human (tele)communications

See also

External links

Richard Hamming

Awards and professional recognition

See also

Books

Quotes

External links and references

Bell Labs

History

Basis

Calculators built by Bell Labs

See also

External links

Electromechanical

See also

Punch card

Origins

Functional details

IBM punch card format

Corner cut

Key punches

Other formats

Advantages

Obsolescence

Dimpled and hanging chads

See also

External links

Nomenclature

See also

Hamming distance

References

See also

1950

Events

January

February

March-April

May-June

July

August-September

October

November

December

Unknown date

Births

January-February

March-April

May-September

October-December