Test Index

JAMB Mathematics 2022 Paper

© africaexams.com

Question : 26

Total: 39

The equivalent of (10110.011)

_{2}

in base 10 is?

26.325
24.372
42.443
22.375

Solution:

Concept:

Convert binary to decimal by expanding each digit as a power of

2

.

Explanation:

Write

(10110.011)_2

in expanded form using powers of

2

.

(10110.011)_2 = (1 \times 2^4) + (0 \times 2^3) + (1 \times 2^2) + (1 \times 2^1) + (0 \times 2^0) + (0 \times 2^{-1}) + (1 \times 2^{-2}) + (1 \times 2^{-3})

.

Evaluate each term.

(1 \times 16) + 0 + (1 \times 4) + (1 \times 2) + 0 + 0 + \left(1 \times \frac{1}{4}\right) + \left(1 \times \frac{1}{8}\right)

.

Add the whole parts:

16 + 4 + 2 = 22

.

Add the fractional parts:

0.25 + 0.125 = 0.375

.

Therefore,

(10110.011)_2 = 22.375

in base

10

.

Answer:

D.

22.375

© africaexams.com

Go to Question:

Prev Question

Next Question