Hexadecimal Numbers
Hexadecimal numbers are numbers represented in base $16$ , which means the digits $0,1,2,3,4,5,6,7,8,9,\text{A,B,C,D,E,F}$ instead of just $0$ - $9$ .
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. (the powers of $10$ ), in base $16$ we have the $1$ s place, $16$ s place, $256$ s place, $4096$ s place, etc. (the powers of $16$ ).
In base $10$ , the number $13$ means one group of $10$ and $3$ ones. In base $16$ , the number $13$ means one group of $16$ and $3$ ones. (This would be equivalent to $19$ in base $10$ .)
Below we count up to $32$ in base $16$ :
BASE $16$ | BASE $10$ |
$0$ | $0$ |
$1$ | $1$ |
$2$ | $2$ |
$3$ | $3$ |
$4$ | $4$ |
$5$ | $5$ |
$6$ | $6$ |
$7$ | $7$ |
$8$ | $8$ |
$9$ | $9$ |
$\text{A}$ | $10$ |
$\text{B}$ | $11$ |
$\text{C}$ | $12$ |
$\text{D}$ | $13$ |
$\text{E}$ | $14$ |
$\text{F}$ | $15$ |
$10$ | $16$ |
$11$ | $17$ |
$12$ | $18$ |
$13$ | $19$ |
$14$ | $20$ |
$15$ | $21$ |
$16$ | $22$ |
$17$ | $23$ |
$18$ | $24$ |
$19$ | $25$ |
$1\text{A}$ | $26$ |
$1\text{B}$ | $27$ |
$1\text{C}$ | $28$ |
$1\text{D}$ | $29$ |
$1\text{E}$ | $30$ |
$1\text{F}$ | $31$ |
$20$ | $32$ |
Hexadecimal numbers are used extensively in computer science.