Final answer:
The decimal representation of signed binary number 10110101 is -106 and for 01110111 it is 119. The conversion process involves using the leftmost bit as the sign indicator and converting the remaining bits as the magnitude to decimal.
Step-by-step explanation:
The question is asking for the decimal representation of signed binary numbers. To convert the signed binary numbers 10110101 and 01110111 to decimal, you need to understand that the leftmost bit represents the sign (0 for positive, 1 for negative) and the remaining bits represent the magnitude in binary.
- a. 10110101: The leftmost bit is 1, which means the number is negative. To find the decimal representation, we first convert the remaining bits 0110101 to decimal, which is 1*2^6 + 1*2^5 + 0*2^4 + 1*2^3 + 0*2^2 + 1*2^1 + 0*2^0, resulting in 64 + 32 + 8 + 2 = 106. Since the original number is negative, the decimal representation is -106.
- b. 01110111: The leftmost bit is 0, indicating this is a positive number. So, simply convert the remaining bits 1110111 to decimal, which gives us 1*2^6 + 1*2^5 + 1*2^4 + 0*2^3 + 1*2^2 + 1*2^1 + 1*2^0, resulting in 64 + 32 + 16 + 4 + 2 + 1 = 119. The decimal representation is thus 119.