Definitions

# Binary code (computing)

Binary code is the system of representing text or computer processor instructions by the use of a two digit number system. This system is composed of only the number zero, representing the off state, and the number one, representing on state, combined in groups of 8. These groups of 8 bits can represent up to 256 different values and can correspond to a variety of different symbols, letters or instructions. An example of this is the uppercase A, which in ASCII binary is 01000001.

In computing and telecommunication, it is used for any of a variety of methods of coding data, such as sequences of characters, into sequences of groups of bits, including fixed-width words or bytes, and variable-length codes such as Huffman code and arithmetic coding.

In a fixed-width binary code, each letter, digit, or other character, is represented by a sequence of bits of the same length, usually indicated in code tables by the octal, decimal or hexadecimal notation for the value of that sequence of bits interpreted as a binary number.

For representing texts in the Latin alphabet often a fixed width 8-bit code is used. The ISO 8859-1 character code uses 8 bits for each character e.g. "R" is "01010010" and "b" is "01100010"; the block of 8 bits is called a byte; it extended the earlier ASCII code, based on the version of the Latin alphabet used for English, which uses 7 bits to represent 128 characters (0–127).

The Unicode standard defines several variable-width encodings and the fixed-width 32-bit (4-byte) UTF-32 code, potentially having room for billions of characters, but using barely more than 1 million combination as definable code points.

A binary sequence can be translated into a decimal number using the following formula, with $y$ being the 1/0:

$\left(2^0 times y\right) + \left(2^1 times y\right) + \left(2^2 times y\right) dots$

Repeat the bracket and increase the exponent for every 1/0 in the sequence. It is important to remember that the formula is used on the sequence from right to left.

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