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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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Previous: Two's-Complement, Integer Fixed-Point Numbers
Next: How Many Bits are Enough for Digital Audio?

written by Julius Orion Smith III
Julius Smith's background is in electrical engineering (BS Rice 1975, PhD Stanford 1983). He is presently Professor of Music and Associate Professor (by courtesy) of Electrical Engineering at Stanford's Center for Computer Research in Music and Acoustics (CCRMA), teaching courses and pursuing research related to signal processing applied to music and audio systems. See http://ccrma.stanford.edu/~jos/ for details.


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