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Representation of Numbers 255
Solution
MATLAB script:
>> x = -7:7
x =
-7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7
>> y = OnesComplement(x,4)
y =
8 9 10 11 12 13 14 0 1 2 3 4 5 6 7
Note that the number 15 is missing since we do not have −0 inour original
array.
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Two’s-complement format The disadvantage of having two codes for
the number 0 is eliminated in this format. Positive numbers are coded as
usual. The B-bit two’s-complement, ˜x, ofapositive integer x is given by
˜x =¯x + 1=2 B − x or x +˜x =2 B (6.31)
where the second equality is obtained from (6.30). Once again, the
MSB of the representation provides the sign bit. Thus, using (6.31) the
two’s-complement format representation 3 is given by
x (2) =
{ x, x ≥ 0
|˜x|, x