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.
BinaryDecimal 
0000(0/4)
0010.25(14)
0100.5(24)
0110.75(34)
100-1(-44)
101-0.75(-34)
110-0.5(-24)
111-0.25(-14)


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