Number base converter

Where each base earns its keep

Nobody converts bases for fun — each base belongs to a place you actually meet it. Hexadecimal is the language of colour codes, MAC addresses, cryptographic hashes and Windows error codes like 0x80070005; when an error report hands you one of those, this page turns it into a decimal you can search for. Binary is where flags, bitmasks and subnet masks live — it is the only base where you can see which individual switches are on. And octal survives almost exclusively in Unix file permissions, where a number like 755 is really three groups of three bits wearing a disguise. Type a value once and the table answers in all four bases at the same time, with the base you typed in shown in bold.

The 53-bit trap in other tools

The quiet danger with long numbers is not this converter — it is the tools around it. Spreadsheets silently mangle integers beyond about fifteen digits (paste a long card or ID number into Excel and watch the tail turn to zeros), and most quick calculators round anything past 53 bits without a word of warning. That matters the moment you convert database IDs, 64-bit timestamps or hash fragments: a value that looks almost right is worse than one that is obviously wrong. Because this page does its arithmetic in arbitrary precision, a 40-digit decimal or a 256-bit hexadecimal value converts exactly, down to the last digit, and a leading minus sign is carried through faithfully. When exactness is the whole point, do the conversion here and only then paste the result onward.

A worked example: reading a chmod, or a bitmask

Try it with the most famous octal number there is: select octal and type 755. The binary line reads 111101101 — split into threes that is 111, 101, 101, which is rwx for the owner and r-x for group and world. Suddenly the permission number explains itself. The same trick decodes any flags value: a status of 0x2C becomes binary 101100, telling you at a glance that bits 2, 3 and 5 are set and the rest are off. This converter is free without limits, like all our developer tools. Two neighbours worth knowing: a HEX colour is simply three base-16 bytes standing shoulder to shoulder — our colour converter reads the whole triplet at once — and the hexadecimal you meet most often in security work comes out of the hash generator.

Reading the same number four ways

A number doesn't change when its base does — only how it's written down. Decimal 255 is FF in hexadecimal (2 digits instead of 3) and 11111111 in binary (the eight bits of one byte, all on). Hex is popular with programmers precisely because each hex digit maps to exactly four bits.