Final answer:
To convert the 8-bit binary number 10110100 to a decimal value, each bit is multiplied by its respective power of 2, and the results are summed. The calculation results in (128 + 32 + 16 + 4), which equals 180. Therefore, the decimal value is 180.
Step-by-step explanation:
To convert the 8-bit binary number 10110100 to a decimal value, we need to understand the place value of each digit. Binary numbers are based on powers of 2, so we assign powers starting from 0 on the far right and increasing by 1 as we move left. Each binary digit (bit) represents a power of 2. To find the decimal value, we multiply each bit by its respective power of 2, and then sum all the values.
- (1 × 27) = 128
- (0 × 26) = 0
- (1 × 25) = 32
- (1 × 24) = 16
- (0 × 23) = 0
- (1 × 22) = 4
- (0 × 21) = 0
- (0 × 20) = 0
Adding these up: 128 + 32 + 16 + 4 = 180.
So, the decimal value of the binary number 10110100 is 180.