| Binary Numeral System |
Article Index for Binary |
Website Links For Binary |
Information AboutBinary Numeral System |
| CATEGORIES ABOUT BINARY NUMERAL SYSTEM | |
| computer arithmetic | |
| elementary arithmetic | |
| positional numeral systems | |
| 2 | |
|
The binary numeral system, or '''base-2 number system''', is a Numeral System that represents numeric values using two symbols, usually 0 and 1 . More specifically, the usual Base - 2 system is a Positional Notation with a Radix of 2. Owing to its straightforward implementation in Electronic Circuit ry, the binary system is used internally by virtually all modern Computer s. HISTORY The ancient Indian Mathematician Pingala presented the first known description of a binary numeral system around 800 BC written in Hindu numerals. The numeration system was based on the Eye Of Horus Old Kingdom numeration system. W. S. Anglin and J. Lambek, ''The Heritage of Thales'', Springer, 1995, ISBN 038794544X online A full set of 8 Trigram s and 64 Hexagram s, analogous to the 3-bit and 6-bit binary numerals, were known to the ancient Chinese in the Classic Text '' I Ching ''. Similar sets of binary combinations have also been used in traditional African divination systems such as Ifá as well as in medieval Western Geomancy . An ordered binary arrangement of the hexagrams of the I Ching , representing the decimal sequence from 0 to 63, and a method for generating the same, was developed by the Chinese scholar and philosopher Shao Yong in the 11th century. However, there is no evidence that Shao understood binary computation. In 1605 .) The modern binary number system was fully documented by Gottfried Leibniz in the 17th century in his article '' Explication De L'Arithmétique Binaire ''. Leibniz's system used 0 and 1, like the modern binary numeral system. In 1854, British mathematician George Boole published a landmark paper detailing a system of Logic that would become known as Boolean Algebra . His logical system proved instrumental in the development of the binary system, particularly in its implementation in electronic circuitry. In 1937, Claude Shannon produced his master's thesis at MIT that implemented Boolean Algebra and binary arithmetic using electronic relays and switches for the first time in history. Entitled '' A Symbolic Analysis Of Relay And Switching Circuits '', Shannon's thesis essentially founded practical Digital Circuit design. In November of 1937, George Stibitz , then working at Bell Labs , completed a relay-based computer he dubbed the "Model K" (for "Kitchen", where he had assembled it), which calculated using binary addition. Bell Labs thus authorized a full research program in late 1938 with Stibitz at the helm. Their Complex Number Computer , completed January 8 , 1940 , was able to calculate Complex Numbers . In a demonstration to the American Mathematical Society conference at Dartmouth College on September 11 , 1940 , Stibitz was able to send the Complex Number Calculator remote commands over telephone lines by a Teletype . It was the first computing machine ever used remotely over a phone line. Some participants of the conference who witnessed the demonstration were John Von Neumann , John Mauchly , and Norbert Wiener , who wrote about it in his memoirs. REPRESENTATION A binary number can be represented by any sequence of Bit s (binary digits), which in turn may be represented by any mechanism capable of being in two mutually exclusive states. The following sequences of symbols could all be interpreted as the same binary numeric value of Love : 0 1 1 0 1 1 0 0 0 1 1 0 1 1 1 1 0 1 1 1 0 1 1 0 0 1 1 0 0 1 0 1 | ||
| :{ Class | "wikitable" |
|
| :{ Class | "wikitable" |
|
| :{ Class | "wikitable" |
|
| :{ Class | "wikitable" |
|
| { Border | 0 cellpadding="8" cellspacing="0" |
|
| { Class | "wikitable" |
|
| { Class | "wikitable" |
|
| { Class | "wikitable" |
|
|
|