Evaluate(111two)\(^2\) and leave your answer in base 2.
A
111001two
B
110001two
C
101001two
D
10010two
Verified Correct Answer: B.
Step-by-Step Mathematical Solution
(111two)\(^2\) change to base 10
(111two)\(^2\) = 1 x 2\(^2\) + 1 x 2\(^1\) + 1 x 2\(^0\) = 4 + 2 + 1 = 7
(111two)\(^2\) = 7\(^2\) = 49 in base 10
convert 49 in base 10 to base 2
2
49
2
24 R 1
2
12 R 0
2
6 R 0
2
3 R 0
2
1 R 1
2
0 R 1
Therefore (111two)\(^2\) = 110001\(_2\)
Or solve by direct multiplication.
Source: Myschool Past Questions Archive (Record #36226)