The decimal equivalent of 10110011_2 is which of the following?

The decimal equivalent of 10110011_2 is which of the following?

• A. 179
• B. 181
• C. 165
• D. 177

Answer: (A)

Binary to decimal conversion relies on the weights of powers of two for each position. For an eight-bit number, the weights from right to left are 2^0, 2^1, 2^2, 2^3, 2^4, 2^5, 2^6, 2^7. In 10110011, the bits that are 1 sit at the positions with weights 2^7, 2^5, 2^4, 2^1, and 2^0. Adding these values gives 2^7 (128) plus 2^5 (32) plus 2^4 (16) plus 2^1 (2) plus 2^0 (1) which sums to 179. So the decimal form is 179. The other options would come from including different powers of two that are not present in this binary pattern.

Binary to decimal conversion relies on the weights of powers of two for each position. For an eight-bit number, the weights from right to left are 2^0, 2^1, 2^2, 2^3, 2^4, 2^5, 2^6, 2^7. In 10110011, the bits that are 1 sit at the positions with weights 2^7, 2^5, 2^4, 2^1, and 2^0. Adding these values gives 2^7 (128) plus 2^5 (32) plus 2^4 (16) plus 2^1 (2) plus 2^0 (1) which sums to 179. So the decimal form is 179. The other options would come from including different powers of two that are not present in this binary pattern.