# 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.