What is the binary representation of decimal 15?

• A. 1110
• B. 1111
• C. 1011
• D. 1001

Answer: (B)

Binary represents numbers as sums of powers of two, with each bit indicating whether a particular power of two is included. For the decimal number 15, look at the powers of two that fit into it: 8, 4, 2, and 1 (these are 2^3, 2^2, 2^1, and 2^0). Since 15 equals 8 + 4 + 2 + 1, all four of these positions are used, so each bit is 1. Writing that in binary gives 1111. You can check by converting back: 1×8 + 1×4 + 1×2 + 1×1 = 15. The other options would correspond to sums like 14, 11, or 9, which don’t add up to 15.