**C**

**Fixed-Point Considerations**

The C6713 is a floating-point processor capable of performing both integer and floating-point operations. Both the C6713 and the A1C23 codec support 2’s-complement arithmetic. It is thus appropriate here to review some fixed-point concepts [1].

In a fixed-point processor, numbers are represented in integer format. In a floating-point processor, both fixed-and floating-point arithmetic can be handled. With the floating-point processor C6713, a much greater range of numbers can be represented than with a fixed-point processor.

The dynamic range of an *N*-bit number based on 2’s-complement representation is between −(2^{N−1}) and (2^{N−1}−1), or between −32,768 and 32,767 for a 16-bit system. By normalizing the dynamic range between −1 and 1, the range will have 2^{N} sections, where 2^{−(N−1)} is the size of each section starting at −1 up to 1 − 2^{−(N−1)}. For a 4-bit system, there would be 16 sections, each of size from −1 to

**C.1 BINARY AND TWO’S-COMPLEMENT REPRESENTATION**

To make illustrations more manageable, a 4-bit system is used rather than a 32-bit word length. A 4-bit word can represent the unsigned numbers 0 through 15, as shown in Table C.1.

The 4-bit unsigned numbers represent a modulo (mod) 16 system. If 1 is added to the largest number (15), the operation wraps ...