#### Answer

$21 = 10101_{\text{two}}$

#### Work Step by Step

The place values for base two are $...,2^5, 2^4, 2^3, 2^2, 2^1, 1$.
The place values that are less than $21$ are $2^4, 2^3, 2^2, 2^1, 1$.
Divide $21$ by $2^4$ or $16$:
$21\div 16 = 1$ remainder $5$
Divide the remainder $5$ by $2^3$ or $8$:
$5 \div 8 = 0$ remainder $5$
Divide the remainder $5$ by $2^2$ or $4$:
$5 \div 4 = 1$ remainder 1
Divide the remainder $2^1$ by $2$:
$1 \div 2 = 0$ remainder $1$
Divide the remainder $1$ by $1$:
$1 \div 1 = 1$
Thus,
$21 = (1 \times 2^4) + (0 \times 2^3) + (1 \times 2^2) +(0 \times 2^1)+ (1 \times 1)
\\21 = 10101_{\text{two}}$