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254 Chapter 6 IMPLEMENTATION OF DISCRETE-TIME FILTERS
For example, using 3 bits, we can represent numbers from −3 to3as
-3 -2 -1 -0 0 1 2 3
-+----+----+----+----+----+----+----+-
100 101 110 111 000 001 010 011
which is a different bit arrangement for negative numbers compared to
the sign-magnitude format.
The advantage of this format is that subtraction can be achieved by
adding the complement, which is very easy to obtain by simply complementing
a number’s bits. However, there are many drawbacks. There are
still two different codes for 0. The addition is a bit tricky to implement,
and overflow management requires addition of the overflow bit to the least
significant bit (or 2 0 ).
MATLAB Implementation The 1s-complement of a positive integer
x using B bits can be obtained by using the built-in function
bitcmp(x,B), which complements the number’s bits. The result is a decimal
number between 0 and 2 B − 1. As before, the dec2bin can be used
to obtain the binary code. Using (6.30), we can develop the MATLAB
function, OnesComplement, which obtains the one’s-complement format
representation. It uses the sign of a number to determine when to use
one’s-complement and can use scalar as well as vector values. The result
is a decimal equivalent of the representation.
function y = OnesComplement(x,B)
% y = OnesComplement(x,B)
% ---------------
% Decimal equivalent of
% Sign-Magnitude format integer to b-bit Ones’-Complement format conversion
%
% x: integer between -2^(b-1) < x < 2^(b-1) (sign-magnitude)
% y: integer between 0