A binary number 1011 equals what decimal value?

A binary number 1011 equals what decimal value?

• A. 9
• B. 11
• C. 10
• D. 13

Answer: (B)

Binary numbers are based on powers of two, with each digit signaling whether to include that power. For 1011, the rightmost bit is 1 (2^0), the next is 1 (2^1), the next is 0 (2^2), and the leftmost is 1 (2^3). Add the powers where there’s a 1: 2^3 + 2^1 + 2^0 = 8 + 2 + 1 = 11. So the decimal value is 11. If the pattern were different, you’d get other values (for example, 1001 would be 9, 1010 would be 10, 1101 would be 13), but this pattern sums to 11.

Binary numbers are based on powers of two, with each digit signaling whether to include that power. For 1011, the rightmost bit is 1 (2^0), the next is 1 (2^1), the next is 0 (2^2), and the leftmost is 1 (2^3). Add the powers where there’s a 1: 2^3 + 2^1 + 2^0 = 8 + 2 + 1 = 11. So the decimal value is 11. If the pattern were different, you’d get other values (for example, 1001 would be 9, 1010 would be 10, 1101 would be 13), but this pattern sums to 11.