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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 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.

2^32^22^12^0
8421
• 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.

2^32^22^12^0
000000
110001
220010
330011
440100
550101
660110
770111
881000
991001
10A1010
11B1011
12C1100
13D1101
14E1110
15F1111

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:

Security+

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

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