binary notation

(′bīn·ə·rē ′nəm·bər ′sis·təm)

(mathematics) A representation for numbers using only the digits 0 and 1 in which successive digits are interpreted as coefficients of successive powers of the base 2. Also known as binary notation; binary system; dyadic number system.

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The use of binary numbers to represent values.

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binary number

A style of expressing numeric values similar to decimal notation except for being based on 2 rather than 10, hence using only the digits 0 and 1, but requiring over three times as many digit positions for a given number, e.g. the number 301 in the decimal system

= 1 × 256	+ 0 × 128	+ 0 × 64	+ 1 × 32	+ 0 × 16	+ 1 × 8	+ 1 × 4	+ 0 × 2	+ 1 × 1
= 1 × 28	+ 0 × 27	+ 0 × 26	+ 1 × 25	+ 0 × 24	+ 1 × 23	+ 1 × 22	+ 0 × 21	+ 1 × 20

is written in binary as 100101101. Just as with the decimal version, the individual positions are called digits, so the binary representation would be said to be of nine digits, against the three digits of the decimal representation 301. To distinguish, one can say binary digits (contracted to ‘bits’) for the one, decimal digits for the other.

Since 8 = 2³ and 16 = 2⁴, both the 8-based octal notation and the 16-based hexadecimal notation effectively group into single graphic characters successive strings of three and four binary digits respectively. Octal notation was once the dominant alternative to the cumbersome pure binary number, but, since the introduction of the byte, hexadecimal has come to predominate.