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JAMB Mathematics 2015 Paper

Question : 41

Total: 61

10011₂ + *****₂ + 11100₂ + 101₂ = 1001111₂

Solution:

Concept:

Convert all binary numbers to base

10

, find the missing value, then convert the result back to binary.

Explanation:

Let the missing binary number be

x_2

Convert the known binary numbers to decimal.

10011_2 = 16 + 2 + 1 = 19

11100_2 = 16 + 8 + 4 = 28

101_2 = 4 + 1 = 5

1001111_2 = 64 + 8 + 4 + 2 + 1 = 79

Now substitute these values into the equation.

19 + x_{10} + 28 + 5 = 79

x_{10} + 52 = 79

x_{10} = 79 - 52 = 27

Convert

27_{10}

back to binary.

27_{10} = 16 + 8 + 2 + 1

Hence,

27_{10} = 11011_2

Answer:

11011_2

So the correct option is B.

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