Which one of the following represents the binary equivalent of the decimal number 25?
11001
A decimal number is converted to binary by dividing repeatedly by 2 and recording the remainder at each step, then reading the remainders from the last upwards.
Dividing 25 by 2 gives 12 with remainder 1. Dividing 12 by 2 gives 6 with remainder 0. Dividing 6 by 2 gives 3 with remainder 0. Dividing 3 by 2 gives 1 with remainder 1. Dividing 1 by 2 gives 0 with remainder 1.
Reading the remainders from the bottom up gives 1, 1, 0, 0, 1, that is 11001.
The result is quickly verified by expanding the binary number using place values, which are powers of two: 1×16 + 1×8 + 0×4 + 0×2 + 1×1 = 16 + 8 + 1 = 25. This check is worth doing because it is fast and catches any slip in the division.
The distractors can be eliminated the same way. Option 10101 expands to 16 + 4 + 1 = 21; option 01101 gives 8 + 4 + 1 = 13; and option 11011 gives 16 + 8 + 2 + 1 = 27. None equals 25.
Hence the binary equivalent of decimal 25 is 11001.
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