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, $\mathrm{10,000}$ 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.