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JAMB Mathematics 2023 Paper

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Question : 12

Total: 80

Divide 1101001

_{two}

_{two}

11101 $_{two}$
111 $_{two}$
10111 $_{two}$
10101 $_{two}$

Solution:

Concept:

Binary division can be solved easily by converting the binary numbers to decimal, dividing, then converting back to binary.

Explanation:

Convert

1101001_{\text{two}}

to decimal:

1 \times 2^6 + 1 \times 2^5 + 0 \times 2^4 + 1 \times 2^3 + 0 \times 2^2 + 0 \times 2 + 1 = 64 + 32 + 8 + 1 = 105

.

Convert

101_{\text{two}}

to decimal:

1 \times 2^2 + 0 \times 2 + 1 = 4 + 1 = 5

.

Divide the decimal values:

105 \div 5 = 21

.

Convert

21

back to binary:

21 = 16 + 4 + 1 = 2^4 + 2^2 + 2^0

, which gives

10101_{\text{two}}

.

So,

1101001_{\text{two}} \div 101_{\text{two}} = 10101_{\text{two}}

.

Answer:

D.

10101_{\text{two}}

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