The sum 11011₂, 1111₂ and 10m10n0₂. Find the value of m and n.

Correct Answer is : m = 0, n = 0

Correct Answer is : m = 0, n = 0

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WAEC Mathematics 2015 Paper

Question : 2

Total: 45

The sum 11011

_2

_2

_2

. Find the value of m and n.

Solution:

Concept:

Add the binary numbers by place value, then compare the result with the given form to find the missing digits.

Explanation:

The complete binary addition is

\mathrm{11011}_2 + \mathrm{1111}_2 + \mathrm{10m10n0}_2 = \mathrm{1110010}_2

First add

\mathrm{11011}_2

and

\mathrm{1111}_2

\mathrm{11011}_2 + \mathrm{1111}_2 = \mathrm{101010}_2

Subtract this from the total sum to get the unknown term:

\mathrm{1110010}_2 - \mathrm{101010}_2 = \mathrm{1001000}_2

Therefore

\mathrm{10m10n0}_2 = \mathrm{1001000}_2

Compare digit by digit:

1\ 0\ m\ 1\ 0\ n\ 0 = 1\ 0\ 0\ 1\ 0\ 0\ 0

Hence

m = 0

and

n = 0

Answer:

Option A:

m = 0

n = 0

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