# 4CB2F   Numbers in other bases   F2BC4

### 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.

Enter number (base 10):

 Choose base: Base 2 Base 3 Base 4 Base 5 Base 6 Base 7 Base 8 Base 9 Base 10 Base 11 Base 12 Base 13 Base 14 Base 15 Base 16 Base 17 Base 18 Base 19 Base 20 Base 21 Base 22 Base 23 Base 24 Base 25 Base 26 Base 27 Base 28 Base 29 Base 30 Base 31 Base 32 Base 33 Base 34 Base 35 Base 36

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### 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 10Base 2Base 3Base 4Base 5Base 8Base 16
1111111
21022222
311103333
41001110444
510112111055
611020121166
711121131277
81000222013108
910011002114119
101010101222012A
111011102232113B
121100110302214C
131101111312315D
141110112322416E
151111120333017F
1610000121100312010
1710001122101322111
1810010200102332212
1910011201103342313
2010100202110402414

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.