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JAMB Mathematics 2024 Paper

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Question : 28

Total: 50

Convert the number 10111.11

_{\text{two}}

to a mixed number.

23 $\;\frac{1}{4}$
23 $\;\frac{3}{4}$
22 $\;\frac{1}{4}$
24 $\;\frac{3}{4}$

Solution:

Concept:

Convert the binary number to base

10

, then write the result as a mixed number.

Explanation:

Split

10111.11_{\text{two}}

into integer part

10111_{\text{two}}

and fractional part

0.11_{\text{two}}

.

Integer part:

10111_{\text{two}} = 1 \times 2^4 + 0 \times 2^3 + 1 \times 2^2 + 1 \times 2^1 + 1 \times 2^0

= 16 + 0 + 4 + 2 + 1 = 23

Fractional part:

0.11_{\text{two}} = 1 \times 2^{-1} + 1 \times 2^{-2}

= \frac{1}{2} + \frac{1}{4} = \frac{3}{4}

Therefore,

10111.11_{\text{two}} = 23 + \frac{3}{4} = 23\frac{3}{4}

.

Answer:

23\frac{3}{4}

(Option B).

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