Convert the decimal number 13 to binary.

• A. 1011
• B. 1110
• C. 10001
• D. 1101

Answer: (D)

Converting a decimal number to binary means expressing the number as a sum of powers of two and writing a 1 for each power that is used, with 0s where it isn’t. For 13, the largest power of two not exceeding it is 8 (2^3). Subtracting 8 leaves 5; the next is 4 (2^2), which fits, leaving 1; the next (2^1) doesn’t fit, so that bit is 0; the smallest power (2^0) is 1, which fits. Reading these bits from 2^3 down to 2^0 gives 1101. So the binary representation is 1101. For reference, 1011 equals 11, 1110 equals 14, and 10001 equals 17, which don’t match 13.