Simplify: (11\(_{two}\))\(^2\)

A.

1001\(_2\)

B.

1101\(_2\)

C.

101\(_2\)

D.

10001\(_2\)

Correct answer is A

(11\(_{two}\))\(^2\) = (11\(_2\) \(\times\) (11\(_2\))

= \({1 \times 2^1 + 1 \times 2^0} \times ({1 \times 2^1 + 1 \times 2^0})\)   

= \({1 \times 2 + 1 \times 1} \times ({1 \times 2 + 1 \times 1})\)

= \({2 + 1} \times ({2 + 1})\)

= 3 \(\times\) 3 

= 9\(_{10}\) or

1001\(_2\) from  

2
2 4 r1
2 2 r0
2 1 r0
  0 r1