5.1.2 Fractional Format

The fractional data format (Qn.m) has integral part (n) and fractional part (m) and the Most Significant bit represents the sign, thus consisting of (m+n+1) bits. It represents a signed two’s complement value. Qn.m format data has a range of [-2ⁿ, (2ⁿ-2^-m)] with 2^-m resolution.

The binary representation of an N-bit (m+n+1 bits) number in Qn.m is shown in Figure 1. The value is given by the equation shown in Figure 2.

Figure 1: Binary Representation

Figure 2: Equation Value