Number base converter (radix)
Number base converter - converts numbers from one number base (radix) to another number base. Calculator supports popular number bases such as decimal (10), hexadecimal (16), binary (2), but also more exotic like ternary (3), hexavigesimal (26) or duosexagesimal (62).

# Inputs data - value and unit, which we're going to convert

 Value Numeral system binary [2]octal [8]decimal [10]hexadecimal [16]binary [2]ternary [3]quaternary [4]quinary [5]senary [6]septenary [7]octal [8]nonary [9]decimal [10]undecimal [11]duodecimal [12]tridecimal [13]tetradecimal [14]pentadecimal [15]hexadecimal [16]base-17 [17]octodecimal [18]base-19 [19]vigesimal [20]base-21 [21]base-22 [22]trivigesimal [23]tetravigesimal [24]base-25 [25]hexavigesimal [26]heptavigesimal [27]base-28 [28]base-29 [29]trigesimal [30]base-31 [31]duotrigesimal [32]tritrigesimal [33]base-34 [34]base-35 [35]hexatrigesimal [36] Decimals 012345678910111213141516171819202122232425262728293031323334353637383940414243444546474849505152535455565758596061626364

# Common bases

 Numeral system Base Value Notes binary 2 1111101000 Position system with base 2. Often called a binary system. The digits in the binary system are 0 and 1. Binary system is the basis for modern computers. octal 8 1750 Position system based on 8 digits. Digit one at the higher position corresponds to the number 8 at the lower position.The pool of digits used in system base 8 (octal system) is: 01234567. decimal 10 1000 Position system with base 10. Often called a decimal system. The digits in the decimal system are 0,1,2,3,4,5,6,7,8 and 9. Decimal system is widely used in everyday life. hexadecimal 16 3e8 Position system with base 16. Often called a hexdecimal system. The digits in the hexdecimal system are 0,1,2,3,4,5,6,7,8,9 and letters a,b,c,d,e,f. Hexdecimal system is often used in software development to present binary data.

# All bases

 Numeral system Base Value Notes binary 2 1111101000 Position system with base 2. Often called a binary system. The digits in the binary system are 0 and 1. Binary system is the basis for modern computers. ternary 3 1101001 Position system based on 3 digits. Digit one at the higher position corresponds to the number 3 at the lower position.The pool of digits used in system base 3 (ternary system) is: 012. quaternary 4 33220 Position system based on 4 digits. Digit one at the higher position corresponds to the number 4 at the lower position.The pool of digits used in system base 4 (quaternary system) is: 0123. quinary 5 13000 Position system based on 5 digits. Digit one at the higher position corresponds to the number 5 at the lower position.The pool of digits used in system base 5 (quinary system) is: 01234. senary 6 4344 Position system based on 6 digits. Digit one at the higher position corresponds to the number 6 at the lower position.The pool of digits used in system base 6 (senary system) is: 012345. septenary 7 2626 Position system based on 7 digits. Digit one at the higher position corresponds to the number 7 at the lower position.The pool of digits used in system base 7 (septenary system) is: 0123456. octal 8 1750 Position system based on 8 digits. Digit one at the higher position corresponds to the number 8 at the lower position.The pool of digits used in system base 8 (octal system) is: 01234567. nonary 9 1331 Position system based on 9 digits. Digit one at the higher position corresponds to the number 9 at the lower position.The pool of digits used in system base 9 (nonary system) is: 012345678. decimal 10 1000 Position system with base 10. Often called a decimal system. The digits in the decimal system are 0,1,2,3,4,5,6,7,8 and 9. Decimal system is widely used in everyday life. undecimal 11 82a Position system based on 11 digits. Digit one at the higher position corresponds to the number 11 at the lower position.The pool of digits used in system base 11 (undecimal system) is: 0123456789a. duodecimal 12 6b4 Position system based on 12 digits. Digit one at the higher position corresponds to the number 12 at the lower position.The pool of digits used in system base 12 (duodecimal system) is: 0123456789ab. tridecimal 13 5bc Position system based on 13 digits. Digit one at the higher position corresponds to the number 13 at the lower position.The pool of digits used in system base 13 (tridecimal system) is: 0123456789abc. tetradecimal 14 516 Position system based on 14 digits. Digit one at the higher position corresponds to the number 14 at the lower position.The pool of digits used in system base 14 (tetradecimal system) is: 0123456789abcd. pentadecimal 15 46a Position system based on 15 digits. Digit one at the higher position corresponds to the number 15 at the lower position.The pool of digits used in system base 15 (pentadecimal system) is: 0123456789abcde. hexadecimal 16 3e8 Position system with base 16. Often called a hexdecimal system. The digits in the hexdecimal system are 0,1,2,3,4,5,6,7,8,9 and letters a,b,c,d,e,f. Hexdecimal system is often used in software development to present binary data. base-17 17 37e Position system based on 17 digits. Digit one at the higher position corresponds to the number 17 at the lower position.The pool of digits used in system base 17 (base-17 system) is: 0123456789abcdefg. octodecimal 18 31a Position system based on 18 digits. Digit one at the higher position corresponds to the number 18 at the lower position.The pool of digits used in system base 18 (octodecimal system) is: 0123456789abcdefgh. base-19 19 2ec Position system based on 19 digits. Digit one at the higher position corresponds to the number 19 at the lower position.The pool of digits used in system base 19 (base-19 system) is: 0123456789abcdefghi. vigesimal 20 2a0 Position system based on 20 digits. Digit one at the higher position corresponds to the number 20 at the lower position.The pool of digits used in system base 20 (vigesimal system) is: 0123456789abcdefghij. base-21 21 25d Position system based on 21 digits. Digit one at the higher position corresponds to the number 21 at the lower position.The pool of digits used in system base 21 (base-21 system) is: 0123456789abcdefghijk. base-22 22 21a Position system based on 22 digits. Digit one at the higher position corresponds to the number 22 at the lower position.The pool of digits used in system base 22 (base-22 system) is: 0123456789abcdefghijkl. trivigesimal 23 1kb Position system based on 23 digits. Digit one at the higher position corresponds to the number 23 at the lower position.The pool of digits used in system base 23 (trivigesimal system) is: 0123456789abcdefghijklm. tetravigesimal 24 1hg Position system based on 24 digits. Digit one at the higher position corresponds to the number 24 at the lower position.The pool of digits used in system base 24 (tetravigesimal system) is: 0123456789abcdefghijklmn. base-25 25 1f0 Position system based on 25 digits. Digit one at the higher position corresponds to the number 25 at the lower position.The pool of digits used in system base 25 (base-25 system) is: 0123456789abcdefghijklmno. hexavigesimal 26 1cc Position system based on 26 digits. Digit one at the higher position corresponds to the number 26 at the lower position.The pool of digits used in system base 26 (hexavigesimal system) is: 0123456789abcdefghijklmnop. heptavigesimal 27 1a1 Position system based on 27 digits. Digit one at the higher position corresponds to the number 27 at the lower position.The pool of digits used in system base 27 (heptavigesimal system) is: 0123456789abcdefghijklmnopq. base-28 28 17k Position system based on 28 digits. Digit one at the higher position corresponds to the number 28 at the lower position.The pool of digits used in system base 28 (base-28 system) is: 0123456789abcdefghijklmnopqr. base-29 29 15e Position system based on 29 digits. Digit one at the higher position corresponds to the number 29 at the lower position.The pool of digits used in system base 29 (base-29 system) is: 0123456789abcdefghijklmnopqrs. trigesimal 30 13a Position system based on 30 digits. Digit one at the higher position corresponds to the number 30 at the lower position.The pool of digits used in system base 30 (trigesimal system) is: 0123456789abcdefghijklmnopqrst. base-31 31 118 Position system based on 31 digits. Digit one at the higher position corresponds to the number 31 at the lower position.The pool of digits used in system base 31 (base-31 system) is: 0123456789abcdefghijklmnopqrstu. duotrigesimal 32 v8 Position system based on 32 digits. Digit one at the higher position corresponds to the number 32 at the lower position.The pool of digits used in system base 32 (duotrigesimal system) is: 0123456789abcdefghijklmnopqrstuv. tritrigesimal 33 ua Position system based on 33 digits. Digit one at the higher position corresponds to the number 33 at the lower position.The pool of digits used in system base 33 (tritrigesimal system) is: 0123456789abcdefghijklmnopqrstuvw. base-34 34 te Position system based on 34 digits. Digit one at the higher position corresponds to the number 34 at the lower position.The pool of digits used in system base 34 (base-34 system) is: 0123456789abcdefghijklmnopqrstuvwx. base-35 35 sk Position system based on 35 digits. Digit one at the higher position corresponds to the number 35 at the lower position.The pool of digits used in system base 35 (base-35 system) is: 0123456789abcdefghijklmnopqrstuvwxy. hexatrigesimal 36 rs Position system based on 36 digits. Digit one at the higher position corresponds to the number 36 at the lower position.The pool of digits used in system base 36 (hexatrigesimal system) is: 0123456789abcdefghijklmnopqrstuvwxyz.

# Some facts

• To write a number in the position system with the basis b, we must present it as a serie containing powers of this base.
${...d_3 d_2 d_1 d_0}_{(b)} = ...(d_3 \times b^3) + (d_2 \times b^2) + (d_1 \times b^1) + (d_0 \times b^0)$
• ⓘ Example: Decimal number 1234 means:
$\underline{\bold{1234}}_{(10)} = (\underline{\bold{1}} \times 10^3) + (\underline{\bold{2}} \times 10^2) + (\underline{\bold{3}} \times 10^1) + (\underline{\bold{4}} \times 10^0)$
• The coefficients for the next base powers are called digits.
• The digit that has the least effect on the value of the number (located at the lowest power) is called the least significant digit. By analogy, the digit whose change most affects the value of the whole number is called the most significant digit.
• It is assumed that we write digits from the most to the least significant order. It means that the most significant digit is on the left hand side and the least significant digit is on the right hand side.
ⓘ Example: Let's get hexadecimal number 12ef(16). The most significant digit is 1, and the least significant one is f.

# Tips & tricks

• Sometimes a number that has an infinite expansion in one system (i.e. it can't be written using a finite number of digits) has a finite expansion in another one. For example, the number 1/3 is the 0.33333333333... (never ending 3333...) in decimal system, but just simple 0.1 in ternary (base 3) one. So the expansion of 1/3 is finite in ternary system.

# How to convert

• Enter the number to field "value" - enter the NUMBER only, no other words, symbols or unit names. You can use dot (.) or comma (,) to enter fractions.
Examples:
• 1000000
• 123,23
• 999.99999
• Find and select your starting unit in field "unit". Some unit calculators have huge number of different units to select from - it's just how complicated our world is...
• And... you got the result in the table below. You'll find several results for many different units - we show you all results we know at once. Just find the one you're looking for.

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