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 2345 is:
Thousands
Hundreds
Tens
Units
2
3
4
5
ie. 2*1000 + 3*100 + 4*10 + 5*1 = 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 0's and 1's.
An example, the value of 1001101 is:
64
32
16
8
4
2
1
1
0
0
1
1
0
1
ie. 64 + 0 + 0 + 8 + 4 + 0 + 1 = 77
A similar procedure is followed for any other base:
Place values depending on Base
Base
6
5
4
3
2
1
5
3125
625
125
25
5
1
7
16807
2401
343
49
7
1
8
32768
4096
512
64
8
1
13
371293
28561
2197
169
13
1
The base value of a number system is the number of different values the set has before repeating itself.
A Base 13 numbering system is represented by:
0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, 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 "equals", to see the result.
