To convert the binary number \(1110\) to base 10, we can use the powers of 2. Each digit in the binary number represents a power of 2, starting from the rightmost digit which is \(2^0\).
The binary number \(1110\) can be broken down as follows:
\[ 1 \times 2^3 + 1 \times 2^2 + 1 \times 2^1 + 0 \times 2^0 \]
Calculating each term:
- \(1 \times 2^3 = 1 \times 8 = 8\)
- \(1 \times 2^2 = 1 \times 4 = 4\)
- \(1 \times 2^1 = 1 \times 2 = 2\)
- \(0 \times 2^0 = 0 \times 1 = 0\)
Now, add these values together:
\[ 8 + 4 + 2 + 0 = 14 \]
Therefore, the binary number \(1110\) in base 10 is \(14\).