JAMB 1992 · UME · Q1

Number bases

Find $n$ if $34_n = 10011_2$ .

Worked solution (try it first)

Change the right side to base ten: $10011_2 = 16 + 2 + 1 = 19$ .
In base $n$ , $34_n = 3n + 4$ , so $3n + 4 = 19$ .
Subtract 4 and divide by 3: $n = 5$ , option A.

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