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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 is fractional fixed point, also in two's complement.

Quite simply, fractional fixed-point numbers are obtained from integer fixed-point numbers by dividing them by $ 2^{N-1}$ . Thus, the only difference is a scaling of the assigned numbers. In the $ N=3$ case, we have the correspondences shown in Table G.5.


Table G.5: 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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``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 © 2014-10-23 by Julius O. Smith III
Center for Computer Research in Music and Acoustics (CCRMA),   Stanford University
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