Binary is a number system that uses only 0s and 1s to represent all real numbers. Each digit represents a power of two. It is a natural system as many things either ‘are’ or ‘aren’t’. Binary systems can be anything that offers only two options. Binary arithmetic is used in electronics and computers. Octal and hexadecimal are base systems widely used in computer applications.
Binary is a number system that uses two numbers to represent all real numbers. While the most common counting system, the decimal system, uses ten numbers, binary uses only 0s and 1s.
Each digit in a binary number system therefore represents a power of two. The first digit on the right represents the 0 power, the second represents the 1st power, the third represents the 2nd power, and so on. So the number 1 in the decimal system is also represented as 1 in the binary system. The number 23, in contrast, is represented as 10111 (16+0+4+2+1).
The decimal system makes perfect sense for humans to use. We have ten fingers and ten toes, so when early humans started counting things they turned to these readily available indicators. Later, when counting systems were codified, it was natural to convert the already used decimal system into a representational system. Binary is also a fairly natural system, however, as many things either ‘are’ or ‘aren’t’. Many spiritualist traditions, such as the Pythagoreans and some Indian mystics, therefore made use of this system, starting from the 6th century BC
In 1854, mathematician George Boole published a central paper on binary systems. This paper laid the foundations for what would eventually be called Boolean algebra. With the advent of electronics, these systems suddenly made incredible sense. Most electronic systems operate on a switch based system, with current on or off. In 1937, Claude Shannon laid the foundations for circuit design theory using binary arithmetic. In 1940, the era of binary computation began with the release of Bell Labs Complex Number Computer, which was capable of performing extremely complex mathematical calculations using this type of system.
In a more general sense, binary systems can be anything that offers only two options, not necessarily limited to number systems. In the case of electronic switches, for example, the system is current-absence. A true-false exam is another example. Yes-no questions are also binary in nature.
There are mathematical methods to transform binary numbers into decimal numbers and vice versa. There are also mathematical devices for performing functions such as addition, subtraction, multiplication and division in several basic systems, including binary. While converting to or from decimal is somewhat cumbersome, converting between binary and octal or hexadecimal, base eight and base 16, respectively, is much easier. This is because both eight and 16 are powers of two, making them well integrated with binary systems. It is for this reason that both octal and hexadecimal are base systems widely used in computer applications.
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