Question 97

Computer Awareness Number representations Easy

What are the positive and negative ranges of number using 12 bits two's complement notation?

(A) \( -2^{11} \) to \( +2^{11}-1 \)
(B) \( -2^{12} \) to \( +2^{12}-1 \)
(C) \( -2^{11} \) to \( +2^{11}-2 \)
(D) \( -2^{11}-1 \) to \( +2^{11} \)
✓ Correct Answer: Option A Verified Solution

📘 Step-by-Step Solution & Detailed Explanation:

With \(n\) bits in 2's complement, the range is \(-2^{n-1}\) to \(2^{n-1} - 1\).

For \(n = 12\): \(-2^{11}\) to \(+2^{11} - 1\), that is, −2048 to +2047.

Answer: (A)

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