What is the decimal value of the 2 's complement representation: \( 00110001_{2} \) \( 153_{10} \) \( 49_{10} \) \( -153_{10} \)

To find the decimal value of the 2's complement representation, we need to follow these steps: 1. Convert the given binary number to decimal. 2. Find the 2's complement of the decimal number. 3. Convert the 2's complement back to decimal. Let's start with the first step: 1. Convert the binary number \( 00110001_{2} \) to decimal: \( 00110001_{2} = 1 \times 2^7 + 0 \times 2^6 + 1 \times 2^5 + 1 \times 2^4 + 0 \times 2^3 + 0 \times 2^2 + 0 \times 2^1 + 1 \times 2^0 \) \( = 128 + 0 + 32 + 16 + 0 + 0 + 0 + 1 \) \( = 177 \) Now, let's find the 2's complement of the decimal number 177: 2. Find the 2's complement of 177: To find the 2's complement, we first convert 177 to binary, then invert all the bits and add 1. \( 177_{10} = 10110001_{2} \) Invert all the bits: \( 01001110_{2} \) Add 1: \( 01001110 + 1 = 01001111 \) \( 01001111_{2} = 183_{10} \) Finally, let's convert the 2's complement back to decimal: 3. Convert the 2's complement \( 01001111_{2} \) to decimal: \( 01001111_{2} = 0 \times 2^7 + 1 \times 2^6 + 0 \times 2^5 + 0 \times 2^4 + 1 \times 2^3 + 1 \times 2^2 + 1 \times 2^1 + 1 \times 2^0 \) \( = 0 + 64 + 0 + 0 + 8 + 4 + 2 + 1 \) \( = 79 \) Therefore, the decimal value of the 2's complement representation \( 00110001_{2} \) is 79.