Convert decimal 15 to binary.

Convert decimal 15 to binary.

• A. 1111
• B. 1100
• C. 1010
• D. 1000

Answer: (A)

Converting decimals to binary uses base-2 place values, where each bit represents a power of two. To make 15, see which powers of two add up to it: 8, 4, 2, and 1. Using all of these means the binary digits in those positions are 1, giving 1111. You can also obtain the same result by dividing by two and recording remainders: 15 → remainder 1, 7 → remainder 1, 3 → remainder 1, 1 → remainder 1, read bottom to top = 1111. The numbers 1100, 1010, and 1000 correspond to 12, 10, and 8, respectively, not 15.

Converting decimals to binary uses base-2 place values, where each bit represents a power of two. To make 15, see which powers of two add up to it: 8, 4, 2, and 1. Using all of these means the binary digits in those positions are 1, giving 1111. You can also obtain the same result by dividing by two and recording remainders: 15 → remainder 1, 7 → remainder 1, 3 → remainder 1, 1 → remainder 1, read bottom to top = 1111. The numbers 1100, 1010, and 1000 correspond to 12, 10, and 8, respectively, not 15.