WAEC 2012 Mathematics · Question 43

Convert 3510 to number in base 2

Options

A.1011
B.10011
C.100011
D.11001

Answer: C. 100011

Explanation written with AI and checked against the answer key

The question reads "3510", which is almost certainly 35₁₀ (35 in base ten), to be converted to base 2. The "10" is the base written in small subscript, and the formatting was lost. Concept To convert a base-10 number to base 2, divide repeatedly by 2 and record the remainders. Then read the remainders from the bottom up. Solution | Division | Quotient | Remainder | |---|---|---| | 35 ÷ 2 | 17 | 1 | | 17 ÷ 2 | 8 | 1 | | 8 ÷ 2 | 4 | 0 | | 4 ÷ 2 | 2 | 0 | | 2 ÷ 2 | 1 | 0 | | 1 ÷ 2 | 0 | 1 | Reading the remainders from the bottom up gives 100011₂. Check: 1×32 + 0×16 + 0×8 + 0×4 + 1×2 + 1×1 = 32 + 2 + 1 = 35 ✓ Answer: Option C, 100011. Tip: Memorise the powers of 2 (1, 2, 4, 8, 16, 32, 64...). For 35, the largest power that fits is 32, and the remainder is 3 = 2 + 1. So put a 1 in the 32, 2 and 1 places and a 0 in the others, which gives 100011. It is quick and a good way to check your answer.

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