What decimal value does the binary number 10000000 represent?

What decimal value does the binary number 10000000 represent?

• A. 8
• B. 64
• C. 256
• D. 128

Answer: (D)

Binary uses place values that double as you move left. In an eight-bit binary number, the bits from right to left represent 2^0, 2^1, 2^2, up to 2^7. In 10000000, the leftmost bit is 1 and all other bits are 0, so the value is 2^7, which equals 128. The other options correspond to different bit positions: 8 would require a 1 in the 2^3 place; 64 is 2^6; 256 would need a ninth bit (a 1 followed by eight zeros), which is outside eight-bit range.

Binary uses place values that double as you move left. In an eight-bit binary number, the bits from right to left represent 2^0, 2^1, 2^2, up to 2^7. In 10000000, the leftmost bit is 1 and all other bits are 0, so the value is 2^7, which equals 128. The other options correspond to different bit positions: 8 would require a 1 in the 2^3 place; 64 is 2^6; 256 would need a ninth bit (a 1 followed by eight zeros), which is outside eight-bit range.