Answer
$111001_{\text{two}}$
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 $57$ are $2^5, 2^4, 2^3$, $2^2$, $2^1$, and $1$
Divide $57$ by $2^5$ or $32$ to obtain:
$57 \div 32 = 1$ remainder $25$
Divide the remainder $25$ by $2^4$ or $16$ to obtain:
$25 \div 16 = 1$ remainder $9$
Divide the remainder $9$ by $2^3$ or $8$ to obtain:
$9 \div 8 = 1$ remainder $1$
Divide the remainder $1$ by $2^2$ or $4$ to obtain:
$1\div 4 = 0$ remainder $1$
Divide the remainder $1$ by $2^1$ or $2$ to obtain:
$1 \div 2 = 0$ remainder $1$
Divide the remainder $1$ by $1$ to obtain:
$1 \div 1 = 1$ remainder $0$
Thus,
$57=(1\times 2^5) + (1 \times 2^4) + (1 \times 2^3) + (0 \times 2^2) + 01 \times 2^1) + (1 \times 1)
\\57=111001_{\text{two}}$