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 C.1.3.

Table C.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)