Writing 45 in base two

Statement

Write the number $45$ in base two (binary).

Solution

Divide repeatedly by $2$, reading the remainders from the bottom: $\begin{aligned} 45 &= 2\cdot 22 + 1, & 22 &= 2\cdot 11 + 0, & 11 &= 2\cdot 5 + 1, \ 5 &= 2\cdot 2 + 1, & 2 &= 2\cdot 1 + 0, & 1 &= 2\cdot 0 + 1. \end{aligned}$ Reading the remainders from last to first: $45 = \boxed{(101101)_2}.$ Check: $32 + 8 + 4 + 1 = 45$.