Fixed-Point Considerations - Digital Signal Processing and Applications with the C6713 and C6416 DSK - page 455

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 sec-

tions, 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 8 from - 1 to 8 .

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 around to give 0 as the answer.
Finite bit systems have the same modulo properties as number wheels on com-
bination locks. Therefore, a number wheel graphically demonstrates the addition