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Binary Numbers

Binary numbers are numbers represented in base $2$ , which means using only the digits $0$ and $1$ .

Just as in base $10$ , we have the $1$ s place, $10$ s place, $100$ s place, $1000$ s place, $10,000$ s place, etc, in base $2$ we have the $2$ s place, $4$ s place, $8$ s place, $16$ s place, etc.

Below we count up to $32$ in base $2$ :

BASE $2$	BASE $10$
$1$	$1$
$10$	$2$
$11$	$3$
$100$	$4$
$101$	$5$
$110$	$6$
$111$	$7$
$1000$	$8$
$1001$	$9$
$1010$	$10$
$1011$	$11$
$1100$	$12$
$1101$	$13$
$1110$	$14$
$1111$	$15$
$10000$	$16$
$10001$	$17$
$10010$	$18$
$10011$	$19$
$10100$	$20$
$10101$	$21$
$10110$	$22$
$10111$	$23$
$11000$	$24$
$11001$	$25$
$11010$	$26$
$11011$	$27$
$11100$	$28$
$11101$	$29$
$11110$	$30$
$11111$	$31$
$100000$	$32$

Binary numbers are used extensively in computer science.