Number Systems Converter
Convert numbers between binary, octal, decimal, hexadecimal, Roman numerals and other bases, with step-by-step working for every conversion.
255 decimal = 11111111 binary
Popular conversions
What is a number system?
A number system is a way of writing numbers with symbols. Everyday numbers use the decimal system, base 10: ten digits (0–9), where each position is worth ten times the one to its right. Other bases work the same way with a different number of digits. Binary (base 2) uses only 0 and 1 and is how computers store everything; hexadecimal (base 16) and octal (base 8) are compact ways for people to write binary.
Roman numerals are different: they are not positional. Letters stand for fixed values (I = 1, V = 5, X = 10, L = 50, C = 100, D = 500, M = 1000) that are added together, with a smaller letter placed before a larger one meaning subtraction (IV = 4, XC = 90).
Every conversion on this site shows its working: place values for reading a number, repeated division for writing it in another base, and symbol-by-symbol tables for Roman numerals.
Numbers 0 to 32 in the main systems
Roman numerals have no zero, so the first row is empty for them.
All 12 number systems
- Binary base 2 255 = 11111111
- Decimal base 10 255 = 255
- Roman numerals 255 = CCLV
- Hexadecimal base 16 255 = FF
- Octal base 8 255 = 377
- Duodecimal base 12 255 = 193
- Ternary base 3 255 = 100110
- Base 36 255 = 73
- Vigesimal base 20 255 = CF
- Quaternary base 4 255 = 3333
- Quinary base 5 255 = 2010
- Senary base 6 255 = 1103
Every conversion
Binary to…
- Binary to decimal
- Binary to Roman numerals
- Binary to hexadecimal
- Binary to octal
- Binary to duodecimal
- Binary to ternary
- Binary to base 36
- Binary to vigesimal
- Binary to quaternary
- Binary to quinary
- Binary to senary
Decimal to…
- Decimal to binary
- Decimal to Roman numerals
- Decimal to hexadecimal
- Decimal to octal
- Decimal to duodecimal
- Decimal to ternary
- Decimal to base 36
- Decimal to vigesimal
- Decimal to quaternary
- Decimal to quinary
- Decimal to senary
Roman numerals to…
- Roman numerals to binary
- Roman numerals to decimal
- Roman numerals to hexadecimal
- Roman numerals to octal
- Roman numerals to duodecimal
- Roman numerals to ternary
- Roman numerals to base 36
- Roman numerals to vigesimal
- Roman numerals to quaternary
- Roman numerals to quinary
- Roman numerals to senary
Hexadecimal to…
- Hexadecimal to binary
- Hexadecimal to decimal
- Hexadecimal to Roman numerals
- Hexadecimal to octal
- Hexadecimal to duodecimal
- Hexadecimal to ternary
- Hexadecimal to base 36
- Hexadecimal to vigesimal
- Hexadecimal to quaternary
- Hexadecimal to quinary
- Hexadecimal to senary
Octal to…
- Octal to binary
- Octal to decimal
- Octal to Roman numerals
- Octal to hexadecimal
- Octal to duodecimal
- Octal to ternary
- Octal to base 36
- Octal to vigesimal
- Octal to quaternary
- Octal to quinary
- Octal to senary
Duodecimal to…
- Duodecimal to binary
- Duodecimal to decimal
- Duodecimal to Roman numerals
- Duodecimal to hexadecimal
- Duodecimal to octal
- Duodecimal to ternary
- Duodecimal to base 36
- Duodecimal to vigesimal
- Duodecimal to quaternary
- Duodecimal to quinary
- Duodecimal to senary
Ternary to…
- Ternary to binary
- Ternary to decimal
- Ternary to Roman numerals
- Ternary to hexadecimal
- Ternary to octal
- Ternary to duodecimal
- Ternary to base 36
- Ternary to vigesimal
- Ternary to quaternary
- Ternary to quinary
- Ternary to senary
Base 36 to…
- Base 36 to binary
- Base 36 to decimal
- Base 36 to Roman numerals
- Base 36 to hexadecimal
- Base 36 to octal
- Base 36 to duodecimal
- Base 36 to ternary
- Base 36 to vigesimal
- Base 36 to quaternary
- Base 36 to quinary
- Base 36 to senary
Vigesimal to…
- Vigesimal to binary
- Vigesimal to decimal
- Vigesimal to Roman numerals
- Vigesimal to hexadecimal
- Vigesimal to octal
- Vigesimal to duodecimal
- Vigesimal to ternary
- Vigesimal to base 36
- Vigesimal to quaternary
- Vigesimal to quinary
- Vigesimal to senary
Quaternary to…
- Quaternary to binary
- Quaternary to decimal
- Quaternary to Roman numerals
- Quaternary to hexadecimal
- Quaternary to octal
- Quaternary to duodecimal
- Quaternary to ternary
- Quaternary to base 36
- Quaternary to vigesimal
- Quaternary to quinary
- Quaternary to senary
Quinary to…
- Quinary to binary
- Quinary to decimal
- Quinary to Roman numerals
- Quinary to hexadecimal
- Quinary to octal
- Quinary to duodecimal
- Quinary to ternary
- Quinary to base 36
- Quinary to vigesimal
- Quinary to quaternary
- Quinary to senary
Senary to…
Frequently asked questions
Why do computers use binary?
Electronic circuits have two reliable states, on and off, which map directly to the digits 1 and 0. Every number, letter, image and instruction in a computer is ultimately stored as binary.
Why do programmers use hexadecimal?
One hexadecimal digit represents exactly four binary digits (bits), so a byte is always two hex digits (00 to FF). Hex is far shorter to read and write than binary and converts to it digit by digit.
Is there a zero in Roman numerals?
No. The Romans had no symbol for zero; medieval scholars sometimes wrote N (for nulla) instead.