Which four-bit binary sequence represents decimal 15?

Which four-bit binary sequence represents decimal 15?

• A. 1110
• B. 1101
• C. 1111
• D. 1011

Answer: (C)

Representing a decimal value in binary uses powers of two for each bit. In four bits the bit values are 8, 4, 2, and 1. To reach 15, you need all of them, so every bit is 1, giving 1111. That equals 8 + 4 + 2 + 1 = 15. The other sequences add up to smaller numbers: 1110 is 14, 1101 is 13, and 1011 is 11. So the four-bit binary sequence for decimal 15 is 1111.

Representing a decimal value in binary uses powers of two for each bit. In four bits the bit values are 8, 4, 2, and 1. To reach 15, you need all of them, so every bit is 1, giving 1111. That equals 8 + 4 + 2 + 1 = 15. The other sequences add up to smaller numbers: 1110 is 14, 1101 is 13, and 1011 is 11. So the four-bit binary sequence for decimal 15 is 1111.