To convert the number \( 1111 \) from base \( 2 \) (binary) to base \( 10 \) (decimal), you can expand it using powers of \( 2 \):
\[ 1111_2 = 1 \cdot 2^3 + 1 \cdot 2^2 + 1 \cdot 2^1 + 1 \cdot 2^0 \]
Calculating each term:
- \( 1 \cdot 2^3 = 1 \cdot 8 = 8 \)
- \( 1 \cdot 2^2 = 1 \cdot 4 = 4 \)
- \( 1 \cdot 2^1 = 1 \cdot 2 = 2 \)
- \( 1 \cdot 2^0 = 1 \cdot 1 = 1 \)
Now, summing these values:
\[ 8 + 4 + 2 + 1 = 15 \]
Thus, \( 1111_2 \) in base \( 10 \) is:
\[ 15_{10} \]