Convert the binary number 10110011 to decimal.

Convert the binary number 10110011 to decimal.

• A. 179
• B. 172
• C. 183
• D. 181

Answer: (A)

Binary numbers use powers of two as place values. For an 8-bit value, the leftmost bit represents 2^7 and the rightmost 2^0. Look at where the bits are 1: in this number the 1s are at positions corresponding to 2^7, 2^5, 2^4, 2^1, and 2^0. Compute those contributions: 2^7 = 128, 2^5 = 32, 2^4 = 16, 2^1 = 2, and 2^0 = 1. Add them up: 128 + 32 + 16 + 2 + 1 = 179. That is the decimal value of 10110011.

Binary numbers use powers of two as place values. For an 8-bit value, the leftmost bit represents 2^7 and the rightmost 2^0. Look at where the bits are 1: in this number the 1s are at positions corresponding to 2^7, 2^5, 2^4, 2^1, and 2^0. Compute those contributions: 2^7 = 128, 2^5 = 32, 2^4 = 16, 2^1 = 2, and 2^0 = 1. Add them up: 128 + 32 + 16 + 2 + 1 = 179. That is the decimal value of 10110011.