The on-and-off voltages manipulated inside a digital computer are, by convention, usually interpreted as "ones" and "zeroes." Strings of ones and zeroes are, by a further act of interpretation, usually held to represent larger numbers. However, no one system of interpretation is mandatory. For example, "0000" is always, in practice, read as decimal 0, and "0001" as decimal 1, but it could have been the other way around. Any mapping of voltages to numbers is, ultimately, arbitrary.

There are practical consequences to this freedom of interpretation. Consider the question of representating positive and negative integers using N bits. N bits allow for 2^N different orderings of ones and zeroes. How should one interpret each of these 2^N strings? There are three basic answers: (1) the sign-and-magnitude (S&M) system, (2) the radix complement system (of which two's complement arithmetic is a special case), and (3) the digit complement system. The first...