GATE Computer Science (CS) 2019 Solved Papers

Question : 18 of 65

Marks: +1, -0

Consider Z = X – Y, where X, Y and Z are all in sign-magnitude form. X and Y are each represented in 𝑛 bits. To avoid overflow, the representation of Z would require a minimum of:

n bits
n - 1 bits
n + 1 bits
n + 2 bits

Validate

Solution:

For example:
Let,

x=+6, n=4

\table X=+6{,}n=4;Y=-5{,}n=4 \}⇒(X-Y)=+11

Hence,
Z = 11 which required 5 bits which is (n+ 1) bits

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