If you're working on a certification exam such as the CompTIA A+, Network+, or Security+ certification, you might need to review your knowledge of decimal, hexadecimal, and binary. It's basic knowledge, but it's needed and I've found that some people never learned it.
Decimal
Decimal numbers use a base of ten and include the numbers 0 to 9.
Hexadecimal
Hexadecimal numbers use a base of 16 and include the numbers 0 to 9 and the characters A to F.
Binary
Binary numbers use a base of 2 and include only the numbers 0 and 1. The following table shows how binary is raised to different powers to give different values in a four bit binary number.
| 2^3 | 2^2 | 2^1 | 2^0 |
|---|---|---|---|
| 8 | 4 | 2 | 1 |
- Any number raised to the power of 0 is 1 so 2^0 is 1.
- Any number raised to the power of 1 is itself so 2^1 is 2
- 2 raised to the power of 2 is the same as 2 x 2 (2 squared or4)
- 2 raised to the power of 3 is the same as 2 x 2 x 2 (2 cubed or 8)
Comparing Numbers
The following table compares each of these number systems side by side.
| Decimal | Hexadcimal | Binary | |||
|---|---|---|---|---|---|
| 2^3 | 2^2 | 2^1 | 2^0 | ||
| 0 | 0 | 0 | 0 | 0 | 0 |
| 1 | 1 | 0 | 0 | 0 | 1 |
| 2 | 2 | 0 | 0 | 1 | 0 |
| 3 | 3 | 0 | 0 | 1 | 1 |
| 4 | 4 | 0 | 1 | 0 | 0 |
| 5 | 5 | 0 | 1 | 0 | 1 |
| 6 | 6 | 0 | 1 | 1 | 0 |
| 7 | 7 | 0 | 1 | 1 | 1 |
| 8 | 8 | 1 | 0 | 0 | 0 |
| 9 | 9 | 1 | 0 | 0 | 1 |
| 10 | A | 1 | 0 | 1 | 0 |
| 11 | B | 1 | 0 | 1 | 1 |
| 12 | C | 1 | 1 | 0 | 0 |
| 13 | D | 1 | 1 | 0 | 1 |
| 14 | E | 1 | 1 | 1 | 0 |
| 15 | F | 1 | 1 | 1 | 1 |
Other Resources
If you plan on taking the A+, Network+ or Security+ exams to give yourself the CompTIA Trio, check out these resources:
