Let's find the decimal equivalent of the binary numbers [tex]\(1100110\)[/tex] and [tex]\(101101\)[/tex], and then perform the subtraction to find the correct answer.
First, convert both binary numbers to their decimal equivalents:
1. The binary number [tex]\(1100110\)[/tex] is converted to decimal:
[tex]\[
1 \cdot 2^6 + 1 \cdot 2^5 + 0 \cdot 2^4 + 0 \cdot 2^3 + 1 \cdot 2^2 + 1 \cdot 2^1 + 0 \cdot 2^0
\][/tex]
[tex]\[
= 64 + 32 + 0 + 0 + 4 + 2 + 0
\][/tex]
[tex]\[
= 102
\][/tex]
2. The binary number [tex]\(101101\)[/tex] is converted to decimal:
[tex]\[
1 \cdot 2^5 + 0 \cdot 2^4 + 1 \cdot 2^3 + 1 \cdot 2^2 + 0 \cdot 2^1 + 1 \cdot 2^0
\][/tex]
[tex]\[
= 32 + 0 + 8 + 4 + 0 + 1
\][/tex]
[tex]\[
= 45
\][/tex]
Now, perform the subtraction:
[tex]\[
102 - 45 = 57
\][/tex]
Thus, the correct answer is:
O A. 57
