Evaluate (101_{two})³

Correct Answer is : 1111101two1111101_{two}1111101two

Correct Answer is : 1111101two1111101_{two}1111101two

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JAMB Mathematics 2022 Paper

Question : 2

Total: 39

Evaluate

(101_{two})^3

Solution:

Concept:

Convert the binary base to base ten, then evaluate the power, and finally convert back to binary.

Explanation:

101_{two} = 1 \times 2^2 + 0 \times 2^1 + 1 \times 2^0 = 4 + 0 + 1 = 5_{ten}

(101_{two})^3 = (5_{ten})^3 = 125_{ten}

Convert

125_{ten}

to binary:

125 = 64 + 32 + 16 + 8 + 4 + 1

This gives

125_{ten} = 1111101_{two}

Answer:

(101_{two})^3 = 1111101_{two}

Correct option: C.

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