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JAMB Mathematics 2018 Paper

Question : 53

Total: 62

if y = 23

_{five}

_{three}

find y leaving your answer in base two

Solution:

Concept:

To add numbers in different bases, first convert each number to base ten, add them, then convert the result to the required base.

Explanation:

Convert

23_{\mathrm{five}}

to base ten:

23_{\mathrm{five}} = (2 \times 5^1) + (3 \times 5^0)

= 10 + 3 = 13

Convert

101_{\mathrm{three}}

to base ten:

101_{\mathrm{three}} = (1 \times 3^2) + (0 \times 3^1) + (1 \times 3^0)

= 9 + 0 + 1 = 10

Add the base ten values:

y = 13 + 10 = 23

Convert

23

to base two:

23 = 16 + 4 + 2 + 1

= 10111_{\mathrm{two}}

Answer:

y = 10111_{\mathrm{two}}

Correct option: B.

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