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JAMB Mathematics 2018 Paper

Question : 5

Total: 62

If y = 23

_{\text{five}}

_{\text{three}}

, find y, leaving your answer in base two

Solution:

Concept:

To add numbers given in different bases, first convert each number to base ten, add them, and then convert the sum back to base two.

Explanation:

Convert

23_{\text{five}}

to base ten:

23_{\text{five}} = 2 \times 5^1 + 3 \times 5^0 = 10 + 3 = 13_{\text{ten}}

Convert

101_{\text{three}}

to base ten:

101_{\text{three}} = 1 \times 3^2 + 0 \times 3^1 + 1 \times 3^0 = 9 + 0 + 1 = 10_{\text{ten}}

Add the base ten values:

y = 13_{\text{ten}} + 10_{\text{ten}} = 23_{\text{ten}}

Convert

23_{\text{ten}}

to base two:

23 = 16 + 4 + 2 + 1

, so

23_{\text{ten}} = 10111_{\text{two}}

Answer:

y = 10111_{\text{two}}

(Option B).

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