**NOTE: THIS DOCUMENT IS OBSOLETE, PLEASE CHECK THE NEW
VERSION:** "Mathematics of the Discrete
Fourier Transform (DFT), with Audio Applications --- Second
Edition", by Julius
O. Smith III, W3K
Publishing, 2007, ISBN 978-0-9745607-4-8. - Copyright ©
*2017-09-28* by Julius O. Smith III -
Center for Computer Research
in Music and Acoustics (CCRMA), Stanford University

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## One’s Complement Fixed-Point Format

One’s Complementis a particular assignment of bit patterns to numbers. For example, in the case of 3-bit binary numbers, we have the assignments shown in Table 4.3.

Table 4.3:Three-bit one’s-complement binary fixed-point numbers.

Binary Decimal 000 0 001 1 010 2 011 3 100 -3 101 -2 110 -1 111 -0

In general, -bit numbers are assigned to binary counter values in the “obvious way” as integers from 0 to , and then the negative numbers are assigned in reverse order, as shown in the example.

The term “one’s complement” refers to the fact that negating a number in this format is accomplished by simply

complementingthe bit pattern (inverting each bit).Note that there are two representations for zero (all 0s and all 1s). This is inconvenient when testing if a number is equal to zero. For this reason, one’s complement is generally not used.