You Only Gave Me One Number?

Number Theory Level 1

1 _ _ _ 2 \Large 1 \, \text{\_}\, \text{\_}\, \text{\_} \, _ 2

The above shows a binary number with the last 3 digits omitted. If this number is divisible by 8, then which of the following must be the last values for these 3 digits (in that order)?

1 , 0 , 0 1,0,0 0 , 1 , 0 0,1,0 0 , 0 , 0 0,0,0 0 , 0 , 1 0,0,1

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Pi Han Goh by Pi Han Goh , 30, Malaysia

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1 solution

Hana Wehbi
May 15, 2016

Relevant wiki: Integer Number Bases

100 0 2 = 1 × 2 3 + 0 × 2 2 + 0 × 2 1 + 0 × 2 0 = 8 ∣ 8 1000_2 = 1\times 2^3 + 0\times2^2 + 0\times 2^1 + 0\times2^0 = 8 | 8

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