Find (101\(_2\))\(^2\), expressing the answer in base 2.
A
11101
B
10101
C
10010
D
11001
Verified Correct Answer: D.
Step-by-Step Mathematical Solution
(101\(_2\))\(^2\) ⇒ 101\(_2\) = 1\times2\(^2\) + 0 \times 2\(^1\) + 1 \times 2\(^0\) = 1 \times 4 + 0 + 1 (Recall x⁰ = 1) = 4 + 1 = 5
(101\(_2\))\(^2\) = (5\(_{10}\))\(^2\) = 25.
25 in base 2 = 11001
Source: Myschool Past Questions Archive (Record #75796)