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