Comparing Decimal, Hexadecimal, and Binary

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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.

2^32^22^12^0
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.

DecimalHexadcimalBinary
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:

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

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