To convert the binary number \(1101\) to base 10, we can use the method of multiplying each digit by \(2\) raised to the power of its position (counting from right to left, starting at \(0\)).
The binary number \(1101\) can be broken down as follows:
- The rightmost digit (1) is in the \(2^0\) place: \(1 \times 2^0 = 1 \times 1 = 1\)
- The next digit (0) is in the \(2^1\) place: \(0 \times 2^1 = 0 \times 2 = 0\)
- The next digit (1) is in the \(2^2\) place: \(1 \times 2^2 = 1 \times 4 = 4\)
- The leftmost digit (1) is in the \(2^3\) place: \(1 \times 2^3 = 1 \times 8 = 8\)
Now, we sum these values:
\[ 1 + 0 + 4 + 8 = 13 \]
Thus, the binary number \(1101\) is equal to the base 10 number \(13\).
The correct response is 13.
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