| 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 circuitry, the binary system is used internally by virtually all modern computers. | |
| The binary number system is the most important one in digital systems, but several others are also important. The decimal system is important because it is universal used to represent quantities outside a digital system. This means that there will be situations where decimal values have to be converted to binary values before they are entered into the digital system. | |
| In additional to binary and decimal, two other number systems find wide-spread applications in digital systems. The octal (base-8) and hexadecimal (base-16) number systems are both used for the same purpose- to provide an efficient means for representing large binary system. | |
| History of Binary Numbering System | |
| The ancient Indian mathematician Pingala presented the first known description of a binary numeral system between the 8th and 4th centuries BC, written in Hindu numerals. The numeration system was based on the Eye of Horus Old Kingdom numeration system. | |
| A full set of 8 trigrams and 64 hexagrams, 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. | |
| In 1605 Francis Bacon discussed a system by which letters of the alphabet could be reduced to sequences of binary digits, which could then be encoded as scarcely visible variations in the font in any random text. | |
| Importantly for the general theory of binary encoding, he added that this method could be used with any objects at all: “provided those objects be capable of a twofold difference only; as by Bells, by Trumpets, by Lights and Torches, by the report of Muskets, and any instruments of like nature”” | |
| The modern binary number system was fully documented by Gottfried Leibniz in the 17th century. 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. | |
| Binary equivalent of different Decimal values | |
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