Simplify: (11\(_{two}\))\(^2\)
MATHEMATICS
WAEC 2021
Simplify: (11\(_{two}\))\(^2\)
- A. 1001\(_2\)
- B. 1101\(_2\)
- C. 101\(_2\)
- D. 10001\(_2\)
Correct Answer: A. 1001\(_2\)
Explanation
(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 | 9 |
| 2 | 4 r1 |
| 2 | 2 r0 |
| 2 | 1 r0 |
| 0 r1 |
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