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WAEC Computer Studies 2022 Paper

Question : 45

Total: 51

The octal fraction 0.65 converts to binary as

Solution:

Concept:

Octal fractions can be converted to binary by first changing to decimal, then converting the decimal fraction to binary.

Explanation:

Write

0.65_8

using octal place values:

0.65_8 = 6 \times 8^{-1} + 5 \times 8^{-2}

= \frac{6}{8} + \frac{5}{64} = \frac{48}{64} + \frac{5}{64} = \frac{53}{64} = 0.828125_{10}

Now convert

0.828125_{10}

to binary by multiplying by

2

repeatedly:

0.828125 \times 2 = 1.65625

→ carry

1

0.65625 \times 2 = 1.3125

→ carry

1

0.3125 \times 2 = 0.625

→ carry

0

0.625 \times 2 = 1.25

→ carry

1

0.25 \times 2 = 0.5

→ carry

0

0.5 \times 2 = 1.0

→ carry

1

Reading the carries from top to bottom gives

0.110101_{2}

Answer:

0.65_8 = 0.110101_2

Correct option: B.

0.110101

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