Discussion
The binary equivalent of the decimal number 26 is
Answer: C
Correct answer: 11010
Dividing repeatedly by two and reading the remainders upward gives the answer. 26 gives remainder 0, then 13 gives 1, then 6 gives 0, then 3 gives 1, then 1 gives 1 - reading upward, 11010. The check is quicker than the derivation: the place values from the left are 16, 8, 4, 2, 1, so 11010 is \[ 16 + 8 + 0 + 2 + 0 = 26. \] An alternative method subtracts the largest power of two that fits and repeats: 26 − 16 = 10, 10 − 8 = 2, 2 − 2 = 0, so the bits at 16, 8 and 2 are set. The distractors are all near misses of the kind produced by reversing the remainder order or dropping a bit, which is why reading the remainders in the right direction matters. In hexadecimal 26 is 1A, and grouping 11010 into fours from the right - 0001 1010 - gives 1 and A directly.
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