Number Base Converter
Validates the digits instead of silently truncating them.
Convert Number Base. Validates the digits instead of silently truncating them. Shows the working, not just the answer.
Digits only for the base you pick — FF for hex, 1011 for binary.
Hexadecimal
FF
255 decimal · 11111111 binary · 8 bits
Every digit is validated against the source base before conversion. That sounds obvious and is not what most converters do — the standard parsing routine stops at the first illegal character and returns whatever it managed, so "1012" read as binary silently becomes 5 instead of an error. Hexadecimal is used in computing because each digit maps to exactly four bits, so the conversion to binary is a lookup rather than arithmetic. One byte is always two hex digits, which is why colours, memory addresses and hashes are all written that way. The bit count is the number of binary digits needed, which is what determines whether a value fits in a given integer type.
How the Number Base Converter works
Convert whole numbers between any bases from 2 to 36, with every digit checked against the source base first. That check is not standard — the usual parsing routine stops at the first illegal character and returns whatever it managed.
Also known as: binary to decimal · hex to decimal converter · decimal to binary converter · what is ff in decimal
Frequently asked questions
How do I convert binary to decimal?
Multiply each digit by its power of two and add. 11111111 is 255. Enter the digits with binary selected as the source base and the calculator does it exactly, rejecting anything containing a 2 or above.
Why is hexadecimal used in computing?
Because each hex digit maps to exactly four bits, so conversion to binary is a lookup rather than arithmetic. One byte is always two hex digits, which is why colours, memory addresses and hashes are all written that way.
What happens if I enter an invalid digit?
The calculator says so. Most converters use a parsing routine that stops at the first illegal character, so "1012" read as binary silently becomes 5 — a wrong answer presented with complete confidence.
What is the highest base I can use?
36, using the digits 0-9 followed by A-Z. Beyond that there are no conventional single characters left, which is why base 64 uses a different scheme entirely rather than continuing the pattern.
How many bits does a number need?
The length of its binary representation, shown here directly. It is what determines whether a value fits in a given integer type — 255 needs 8 bits and fits a byte; 256 needs 9 and does not.
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