# Fractional Binary Fixed-Point Numbers

## GUIDE: Mathematics of the Discrete Fourier Transform (DFT) - Julius O. Smith III. Fractional Binary Fixed-Point Numbers

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NOTE: THIS DOCUMENT IS OBSOLETE, PLEASE CHECK THE NEW VERSION: "Mathematics of the Discrete Fourier Transform (DFT), with Audio Applications --- Second Edition", by Julius O. Smith III, W3K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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## Fractional Binary Fixed-Point Numbers

In ''DSP chips'' (microprocessors explicitly designed for digital signal processing applications), the most commonly used fixed-point format isfractional fixed point, also in two's complement.

Quite simply, fractional fixed-point numbers are obtained from integer fixed-point numbers by dividing them by . Thus, the only difference is a scaling of the assigned numbers. In the case, we have the correspondences shown in Table 4.6.

Table 4.6:Three-bit fractional fixed-point numbers.
 Binary Decimal 000 0 (0/4) 001 0.25 (1/4) 010 0.5 (2/4) 011 0.75 (3/4) 100 -1 (-4/4) 101 -0.75 (-3/4) 110 -0.5 (-2/4) 111 -0.25 (-1/4)

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