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

Q. 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

Ans: 𝑛 + 1 bits

Solution:

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.