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WAEC Mathematics 2021 Paper

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Question : 2

Total: 49

Simplify: (11

_{\text{two}}

^{2}

1001 $_{2}$
1101 $_{2}$
101 $_{2}$
10001 $_2$

Solution:

Concept:

Convert the binary number to decimal, square it, then convert back to binary.

Explanation:

First, write

11_{\text{two}}

in base 10.

11_{\text{two}} = 1 \times 2^{1} + 1 \times 2^{0}

= 2 + 1 = 3

So,

(11_{\text{two}})^{2} = 3^{2} = 9

Now convert

9

back to binary.

9 = 8 + 1 = 1 \times 2^{3} + 0 \times 2^{2} + 0 \times 2^{1} + 1 \times 2^{0}

Therefore,

9_{10} = 1001_{\text{two}}

Answer:

(11_{\text{two}})^{2} = 1001_{2}

Correct option: A.

1001_{2}

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