Computer Math, Part 4: Hexadecimal
Now that you understand binary, let’s move onto hexadecimal, or base 16. This is the numbering system most programmers use, because it translates easily to and from binary. Also, 2 hexadecimal digits make up a byte, or 8 bits.
How do we have 16 digits? Simple, hexadecimal uses the digits 0-9 and the letter A-F. 0-9 is the same in hexadecimal as decimal. The digits A-F in hexadecimal are 10-15 in decimal. Here is a conversion chart of single digit hexadecimal:
| Hexadecimal | Binary | Decimal |
|---|---|---|
| 016 | 02 | 010 |
| 116 | 12 | 110 |
| 216 | 102 | 210 |
| 316 | 112 | 310 |
| 416 | 1002 | 410 |
| 516 | 1012 | 510 |
| 616 | 1102 | 610 |
| 716 | 1112 | 710 |
| 816 | 10002 | 810 |
| 916 | 10012 | 910 |
| A16 | 10102 | 1010 |
| B16 | 10112 | 1110 |
| C16 | 11002 | 1210 |
| D16 | 11012 | 1310 |
| E16 | 11102 | 1410 |
| F16 | 11112 | 1510 |
Hexadecimal, sometimes simply called hex, is very easy to translate to and from binary. This is because each digit in hex is 4 digits in binary. All you have to do is replace the hexadecimal digit with the binary equivalent. For instance, the number FF16 is 111111112.
Converting a binary number to hex works just slightly different. When you convert a number from hex to binary, you can work from left to right or right to left. When you convert a number from binary to hex, you must work from right to left. This is because a binary number might not be the correct length to work from left to right.
That’s all for today, check back Friday for Octal, or base 8. Here’s some homework:
Convert the following hexadecimal numbers to binary and decimal:
A216
FFFFFF16
10016
CCCCCC16
A2B16
FA6F16
12316
32116
100016
1000016
