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5 Answers

Best answer
55 votes
55 votes
Let $X$ and $Y$ represents $31$ and $- 31$ respectively in binary sign magnitude form. $X$ and $Y$ will take $6$ bits as range of sign magnitude form is $-\left(2^{(n-1)}-1\right)$ to $2^{(n-1)}-1$; where $n$ is the number of bits.

Now in question $Z= X-Y$,

$Z = 31 - (-31) = 62$

To represent $62$ in sign magnitude form we need $7\;( 6+1)$ bits.

Hence, $n+1$ bits needed.

Answer is $C$.
edited by
15 votes
15 votes
No overflow if two number with opposite sign are added.
Here $(X+(-Y))$ wont give any overflow if sign of $X$ and $-Y$ are opposite else it may cause overflow.
Nothing mentioned in question so in worst case it will give overflow.

Additional bit needed to handle overflow.
Total $n+1$ bits needed.
edited by
7 votes
7 votes

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.

 

https://www.geeksforgeeks.org/gate-cs-2019/

Answer:

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