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Count with numbers in bases other than ten
How numbers in other bases work
Number convertor

Count with numbers in bases other than ten

We usually use Arabic numbers, which are base 10, or decimal. Computers use binary, which is base 2. This page deals with numbers in other bases. Enter a number to convert it to a different base, or count in a base.

How numbers in other bases work

In Arabic numbers (decimal, or base 10), there are 10 digits: 0,1,2,3,4,5,6,7,8,9. You need one digit each to count up to 9, but two digits for ten, and three digits for a hundred, which is ten times ten. In Binary, base 2, you need two digits for two, as you only have two digits, 0 and 1. Base 5 has five digits, and the number five becomes 10. For base 16, you will need sixteen digits, and there are only ten numerals. So we use the letters A,B,C,D,E,F. These represent the decimal numbers 10, 11, 12, 13, 14 and 15. Look at the table below and find the pattern for these bases.

Base 10	Base 2	Base 3	Base 4	Base 5	Base 8	Base 16
1	1	1	1	1	1	1
2	10	2	2	2	2	2
3	11	10	3	3	3	3
4	100	11	10	4	4	4
5	101	12	11	10	5	5
6	110	20	12	11	6	6
7	111	21	13	12	7	7
8	1000	22	20	13	10	8
9	1001	100	21	14	11	9
10	1010	101	22	20	12	A
11	1011	102	23	21	13	B
12	1100	110	30	22	14	C
13	1101	111	31	23	15	D
14	1110	112	32	24	16	E
15	1111	120	33	30	17	F
16	10000	121	100	31	20	10
17	10001	122	101	32	21	11
18	10010	200	102	33	22	12
19	10011	201	103	34	23	13
20	10100	202	110	40	24	14

All these bases are positional, like Arabic numbers (base 10).

Number convertor

Change the number bases if you want to, and then enter a number in one of the boxes. The number will be converted to the different bases. If your number is in a base greater than 10, remember that some digits may be letters. These should be capital letters as it won't recognise lower case.

The common number bases are decimal numbers (Arabic numbers) or base 10, and binary or base 2.
Hexadecimal (base 16) and octal (base 8) are sometimes used in programming, as a short-hand for binary.
All these different bases are positional systems, like Arabic numbers. They all have a zero, unlike older number systems.