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Number Base Converter

The decimal system is perhaps, the best known of the number systems. It got its name because it is a base-ten system. The value of each place is ten times greater than the value of the place just to its right. A thousand is 10 times 100; a hundred is 10 times 10; ten is 10 times 1.

For example, the value of 2,345 is:

 
Thousands Hundreds Tens Units
2 3 4 5
 
ie. 2x1000 + 3x100 + 4x10 + 5x1 = 2,345
 
On the other hand, the computer uses the binary numbering system. Here, the value of each place is two times greater than the value of the place just to its right. Binary means two thus the system is represented by 0s and 1s.

An example, the value of 1001101 is:

 
64 32 16 8 4 2 1
1 0 0 1 1 0 1
 
(64x1) + (32x0) + (16x0) + (8x1) + (4x1) + (2x0) + (1x1) = 77
 
A similar procedure is followed for any other base:
 
Place values depending on Base
Base/Level 6 5 4 3 2 1
5 3,125 625 125 25 5 1
7 16,807 2,401 343 49 71
8 32,768 4,096 512 64 8 1
13 371,293 28,561 2,197 169 13 1
 
The base value of a number system is the number of different values the set has before repeating itself.

That means the higher the base the lower the number of digits required to represent a number.

The reverse is inversely true; the lower the base, the higher the number of digits required to represent the number.

  • A Base 13 numbering system is represented by 0 - 9, A - C
  • Binary has 2 base values(0, 1)
  • Decimal has 10 base values(0 - 9)
  • Octal has 8 base values(0 - 7)
  • Duodecimal has 12 base values(0 - 9, A - B)
  • Hexadecimal has 16 base values(0 - 9, A-F)

Below, input any decimal number; choose the base (up to 36); press "Get Results", to see the result.

 
Convert Base







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