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 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**.