Number of Binary Digits in Power of 10/Example/1000

Theorem
When expressed in binary notation, the number of digits in $1000$ is $10$.

Proof
Let $m$ be the number of digits in $1000$.

We have that $1000$ is not a power of $2$.

From Number of Binary Digits in Power of 10:
 * $m = \left\lceil{3 \log_2 10}\right\rceil$

From Logarithm Base 2 of 10:
 * $\log_2 10 \approx 3 \cdotp 32192 \, 8 \ldots$

and so:
 * $m \approx 9.96$

Hence the result.

The actual number is:
 * $1000_{10} = 1 \, 111 \, 101 \, 100_2$