The range of integers that can be... - Solved

Question 50

Computer Awareness Number representations Hard

The range of integers that can be represented by a 2 's complements number system is. where \( n \) is number of bits in number.

(A) \( -2^{\mathrm{n}-1} \) to \( 2^{\mathrm{n}-1}-1 \)

(B) \( -\left(2^{\mathrm{n}-1}-1\right) \operatorname{to}\left(2^{\mathrm{n}-1}-1\right) \)

(C) \( -2^{\mathrm{n}-1} \) to \( 2^{\mathrm{n}-2} \)

(D) \( -\left(2^{\mathrm{n}-1}+1\right) \) to \( \left(2^{\mathrm{n}-1}-1\right) \)

✓ Correct Answer: Option A Verified Solution

With \(n\) bits in 2's complement, the most significant bit has weight \(-2^{n-1}\).

Example: for 8 bits, the range is −128 to +127.

Answer: (A) \(-2^{n-1}\) to \(2^{n-1}-1\)

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