Comparing Decimal, Hexadecimal, and Binary
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 numbering systems. This is basic knowledge, but it’s important. If you haven’t used these numbering systems in a while, they might be a little foggy.
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 or 4)
- 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 |
Try This
See if you convert the following hexadecimal numbers to four binary bits:
- 5
- 7
- B
- E
See if you convert the following decimal numbers to hexadecimal:
- A
- C
- D
- F
See if you convert the following decimal numbers to four binary bits:
- 4
- 8
- 9
- 14
Other Resources
If you plan on taking the A+, Network+ or Security+ exams to give yourself the CompTIA Trio, check out these resources:
A+
Network+
Security+
Conversion Answers
The following hexadecimal numbers converted to four binary bits are:
- 5 is 0101
- 7 is 0111
- B is 1011
- E is 1110
The following hexadecimal numbers converted to decimal are:
- A is 1010
- C is 1100
- D is 1101
- F is 1111
The following decimal numbers converted to four binary bits are:
- 4 is 0100
- 8 is 1000
- 9 is 1001
- 14 is 1110
