GATE | GATE CS 2019 | Question 15

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:

(A) n bits
(B) n−1 bits
(C) n+1 bits
(D) n+2 bits


Answer: (C)

Explanation: Overflow can occur when two same sign numbers are added or two opposite sign numbers are subtracted.

For example:

let n = 4 bit, X = +6 and Y = -5 (1 bit for sign and 3 bit for magnitude)
Therefore, Z = X - Y = 6 - (-5) = 6+5 = 11
But result (Z) 11 needs 5 (= 4 + 1) bits to store, 
Sin integer 11 needs 1 bit for sign and 4 bit for magnitude. 

Therefore, to avoid overflow, the representation of Z would require a minimum of (n + 1) bits.



Option (C) is correct.


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