# Binary & Integer representation of data

An integer is any whole number or its negative counterpart (e.g. 2, 7, 241, 0, −35, −1022). All modern digital systems represent integer quantities using binary numeration, where integer numbers consist of strings of “bits,” each bit having two possible values: 0 or 1. Unlike the decimal numeration system, most people are familiar with where the place-weight values are powers of ten, the place-weight values of binary numeration are powers of two. The following example shows how the integer number six hundred and three is represented in both decimal and binary formats:

The largest integer value representable in any positive place-weighted format is the base raised to the power of the number of places, minus one. So, for a three-digit decimal number, the largest possible value is 103 − 1 (1000 − 1 = 999). For a ten-bit binary number, the largest possible value is 210 − 1 (1024 − 1 = 1023).

The beauty of binary representation is that the individual “bits” are easy to encode in physical form. “1” and “0” values may take the form of voltage levels (“high” or “low”) in an electronic circuit, magnetization states on a magnetic disk or magnetic tape, AC signal frequencies (“high” or “low”) transmitted on a two-conductor cable, pulses of light transmitted through a fiber optic cable, or any other medium capable of representing two different states. This makes binary a natural form of numerical representation for computers.

Hossein Tootoonchy