Binary

Astronomy

A stellar system that consists of two nearby stars that revolve against a common center of gravity.

See also [Binary stars]?, Optical binary.

Mathematics and Computer Science

Base two: a number representation consisting of zeroes and ones. It is used by practically all computers because of its ease of implementation using digital electronics and Boolean algebra.

As in all place-based number systems, the location of each digit is significant. The right most digit (or the first digit to the left of the decimal point if the number contains a decimal point) corresponds to the ones-place (2⁰ = 1) and the value represented by that digit is simply the digit (1 or 0) multiplied by 1. The digit to the left of the one-place corresponds to the 2¹-place, so that digit represents (1 or 0) multiplied by 2¹. The next digit corresponds to 2² (= 4) and so on. Digits to the right of the decimal place correspond to 2^-1, 2^-2, ...

To obtain the Decimal equivalent of a binary number, simply multiply the various digits by their appropriate place-values and add the results together. For example:

101101001 = 1×2⁸ + 0×2⁷ + 1×2⁶ + 1×2⁵ + 0×2⁴ + 1×2³ + 0×2² + 0×2¹+ 1×2⁰ = 256 + 64 + 32 + 8 + 1 = 361

101.011 = 1×2² + 0×2¹ + 1×2⁰ + 0×2^-1 + 1×2^-2 + 1×2^-3 = 4 + 1 + 0.25 + 0.125 = 5.375

To convert from an integer decimal number to its binary equivalent, divide the number by two and place the remainder in the ones-place. Divide the result by two and place the remainder in the next place to the left. Continue until the result is zero. For example:

Operation	Remainder	Result
118/2 = 59	0	0
59/2 = 29	1	10
29/2 = 14	1	110
14/2 = 7	0	0110
7/2 = 3	1	10110
3/2 = 1	1	110110
1/2 = 0	1	1110110

giving a final result of 1110110.

See also Register, Decimal, Hexadecimal, Octal, Floating point.