A binary number 1100 equals which decimal value?

A binary number 1100 equals which decimal value?

• A. 9
• B. 10
• C. 14
• D. 12

Answer: (D)

In binary, each position represents a power of two, with the rightmost bit as 2^0, then 2^1, 2^2, and so on. For 1100, the bits align with 2^3, 2^2, 2^1, 2^0, giving weights 8, 4, 2, 1. Multiply and add: 1×8 + 1×4 + 0×2 + 0×1 = 8 + 4 + 0 + 0 = 12. So the decimal value is 12. If it were 1001, you’d get 9; 1010 would be 10; 1110 would be 14, illustrating how the positions determine the total.

In binary, each position represents a power of two, with the rightmost bit as 2^0, then 2^1, 2^2, and so on. For 1100, the bits align with 2^3, 2^2, 2^1, 2^0, giving weights 8, 4, 2, 1. Multiply and add: 1×8 + 1×4 + 0×2 + 0×1 = 8 + 4 + 0 + 0 = 12. So the decimal value is 12. If it were 1001, you’d get 9; 1010 would be 10; 1110 would be 14, illustrating how the positions determine the total.