Which binary string represents decimal 15?

Which binary string represents decimal 15?

• A. 1010
• B. 1110
• C. 1111
• D. 1001

Answer: (C)

In binary, each digit represents a power of two, from right to left: 1, 2, 4, 8, etc. To represent 15, you need the 8, 4, 2, and 1 positions all set to 1. That gives the string 1111, which equals 8 + 4 + 2 + 1 = 15. The other strings don’t reach 15: 1010 equals 8 + 2 = 10; 1110 equals 8 + 4 + 2 = 14; 1001 equals 8 + 1 = 9. So 1111 is the correct binary representation of 15.

In binary, each digit represents a power of two, from right to left: 1, 2, 4, 8, etc. To represent 15, you need the 8, 4, 2, and 1 positions all set to 1. That gives the string 1111, which equals 8 + 4 + 2 + 1 = 15.

The other strings don’t reach 15: 1010 equals 8 + 2 = 10; 1110 equals 8 + 4 + 2 = 14; 1001 equals 8 + 1 = 9. So 1111 is the correct binary representation of 15.