Convert the binary number 1011 to base 10.

Step 1: A power of 10 is written as $10^{k} = 1$ followed by $k$ zeros.

For $k = 112$, $10^{112}$ is 1 followed by 112 zeros.

Step 2: The total number of digits is the digit 1 plus the 112 zeros.

$1 + 112 = 113$

Alternatively, using the formula for the number of digits $d$ in $n > 0$:

$d = \lfloor \log_{10} n \rfloor + 1$

Substitute $n = 10^{112}$:

$\log_{10} (10^{112}) = 112$

$\lfloor 112 \rfloor + 1 = 112 + 1 = 113$

10^{112} has 113 digits.

$\boxed{113}$