To convert the binary number 1101 to its base 10 equivalent, you can use the positional value of each digit. In binary, each digit represents a power of 2 based on its position from right to left, starting at 0.
For the binary number 1101:
- The rightmost digit (1) is in the 2^0 position, which is 1.
- The next digit (0) is in the 2^1 position, which is 0.
- The next digit (1) is in the 2^2 position, which is 4.
- The leftmost digit (1) is in the 2^3 position, which is 8.
Now, we add these values together:
\[ 1 \times 2^3 + 1 \times 2^2 + 0 \times 2^1 + 1 \times 2^0 = 1 \times 8 + 1 \times 4 + 0 \times 2 + 1 \times 1 \]
Calculating that gives:
\[ 8 + 4 + 0 + 1 = 13 \]
So, the binary number 1101 in base 10 is 13.
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