Answer
$111111_{\text{two}}$
Work Step by Step
The place values of base two are: $...,2^5, 2^4, 2^3, 2^2, 2^1, 1$.
The place values that are less than or equal to $63$ are $2^5, 2^4, 2^3$, $2^2$, $2^1$, and $1$
Divide $63$ by $2^5$ or $32$ to obtain:
$63 \div 32 = 1$ remainder $31$
Divide the remainder $31$ by $2^4$ or $16$ to obtain:
$31 \div 16 = 1$ remainder $15$
Divide the remainder $15$ by $2^3$ or $8$ to obtain:
$15 \div 8 = 1$ remainder $7$
Divide the remainder $7$ by $2^2$ or $4$ to obtain:
$7\div 4 = 1$ remainder $3$
Divide the remainder $3$ by $2^1$ or $2$ to obtain:
$3 \div 2 = 1$ remainder $1$
Divide the remainder $1$ by $1$ to obtain:
$1 \div 1 = 1$ remainder $0$
Thus,
$63=(1\times 2^5) + (1 \times 2^4) + (1 \times 2^3) + (1 \times 2^2) + (1 \times 2^1) + (1 \times 1)
\\63=111111_{\text{two}}$
