which of the following 7 - bit binary numbers represents a speed of 63 miles per hour?\na 0011111\nb…

Explanation:

Step1: Convert binary to decimal

For a binary number (a_{n}2^{n}+a_{n - 1}2^{n - 1}+\cdots+a_{1}2^{1}+a_{0}2^{0}), where (a_{i}) is either 0 or 1. For option A: (0011111) in decimal is (0\times2^{6}+0\times2^{5}+1\times2^{4}+1\times2^{3}+1\times2^{2}+1\times2^{1}+1\times2^{0}=16 + 8+4 + 2+1=31).

Step2: Option B conversion

For (0101111) in decimal is (0\times2^{6}+1\times2^{5}+0\times2^{4}+1\times2^{3}+1\times2^{2}+1\times2^{1}+1\times2^{0}=32+8 + 4+2 + 1=47).

Step3: Option C conversion

For (0111111) in decimal is (0\times2^{6}+1\times2^{5}+1\times2^{4}+1\times2^{3}+1\times2^{2}+1\times2^{1}+1\times2^{0}=32+16 + 8+4 + 2+1=63).

Step4: Option D conversion

For (1010101) in decimal is (1\times2^{6}+0\times2^{5}+1\times2^{4}+0\times2^{3}+1\times2^{2}+0\times2^{1}+1\times2^{0}=64 + 16+4 + 1=85).

Answer:

C. 0111111