JAMB 2017 · UTME (set 2) · Q16✱✱

Number bases

The addition below was carried out in a certain base.

$\begin{array}{rr} & 1101.01 \\ + & 1110.11 \\ & 1011.10 \\ \hline & 100111.10 \end{array}$

The base in which the operation was performed was

Worked solution (try it first)

Every digit is 0 or 1, so try base 2 first.
In base 2: $1101.01 = 13.25$ , $1110.11 = 14.75$ and $1011.10 = 11.5$ .
Their sum is $39.5$ .
The answer $100111.10_2$ is $32 + 4 + 2 + 1 + 0.5 = 39.5$ , which matches.
So the base is 2, option B.

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