Question

The binary number 1101 is equal to which base 10 number? (1 point) Responses 11 11 12 12 13 13 14

Answer 1

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**.