Fractional Binary Fixed-Point Numbers

GUIDE: Mathematics of the Discrete Fourier Transform (DFT). Fractional Binary Fixed-Point Numbers

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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 $2^{N-1}$. Thus, the only difference is a scaling of the assigned numbers. In the $N=3$ case, we have the correspondences shown in Table 4.6.


Table 4.6:Three-bit fractional fixed-point numbers.
Binary Decimal  
000 0 (0/4)
001 0.25 (14)
010 0.5 (24)
011 0.75 (34)
100 -1 (-44)
101 -0.75 (-34)
110 -0.5 (-24)
111 -0.25 (-14)

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