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Convert the binary number 1011 to base 10.

March 18, 2026Mathematics

ScanSolve AI Answer

Answer

113

Step-by-step solution

2 steps

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.
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.
$113$

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