Number Base Converter

Type one number per line and each one gets its own block of results, so you can convert a whole list in one go.

1. Enter your numbers in the input box, one per line. Spaces, commas and underscores inside a number are ignored, so 1_000 and 1,000 read as one thousand.
2. Choose Input base. Auto reads the prefixes 0x (hexadecimal), 0b (binary) and 0o (octal), and treats anything else as decimal. Or fix the base yourself: Binary (2), Octal (8), Decimal (10), Hexadecimal (16), Base 32 or Base 36.
3. Read the block under each number: Binary grouped in fours, Octal, Decimal, Hexadecimal in capitals, Base 32 and Base 36.
4. If a digit does not belong in the chosen base, the line names it, for example that 9 is not a valid digit in base 8, and the other lines still convert.

Every base is positional: each digit is multiplied by a power of the base and the products are added. Take 255. In hexadecimal, FF means 15 × 16 + 15 = 255. In octal, 377 means 3 × 64 + 7 × 8 + 7 = 255. In binary, 1111 1111 is 128 + 64 + 32 + 16 + 8 + 4 + 2 + 1 = 255. Going the other way, you divide repeatedly by the target base and read the remainders from last to first.

Base 32 and base 36 follow the same rule with a longer digit set. In base 36 the letters stand for the values 10 to 35, so Z is 35. The number 255 equals 7 × 36 + 3, which is why it is written 73. That is a handy cross-check when you want to confirm a result by hand.

The last row shows why exact integer arithmetic matters: a number that large cannot be held precisely in an ordinary floating-point value, but this tool keeps every digit.

Binary shows what the hardware stores, and grouping in fours makes it line up with hexadecimal, since one hex digit is exactly four bits. That is why bit masks, memory addresses and byte values are written in hex. Web colours are hex too: the pair FF in #FF8800 is 255 of red, which you can confirm with the Hexadecimal setting, or explore further in the colour picker.

Octal survives in Unix file permissions. The command chmod 755 uses the octal digits 7, 5, 5, which equal decimal 493 and binary 111 101 101. Enter 0o755 in Auto mode to see all three. Base 36 uses the digits 0-9 and then A-Z, which makes it a compact way to shorten numeric IDs. For text rather than numbers, the hex to text converter and the binary code translator translate bytes into readable characters, and the hash generator produces the long hex strings you may want to inspect.

• Whole numbers only. Fractions and floating-point values such as 0.5 or 1e3 are not accepted.
• Negative numbers keep their minus sign, so -255 shows -FF. Two's complement, the fixed-width form that hardware uses for negatives, is not produced.
• The input can be up to 200 digits long.
• Base 32 here uses the digits 0-9 followed by A-V. This is not the A-Z and 2-7 alphabet used by the Base32 text encoding, so the two will not match.
• Prefixes are only honoured when they agree with the base you chose. With Decimal selected, 0xFF is an error rather than 255.
• Letters are case-insensitive on input, so ff, Ff and FF are the same hexadecimal number. Output letters are always capitals.

Because each line gets its own block, it is easy to compare related values side by side. Try 15, 16 and 255 with the Auto setting to see where a hexadecimal number gains an extra digit, or paste a column of byte values to check them against a datasheet. When a result looks wrong, first check the Input base: the same digits 101 mean 5 in binary, 65 in octal and 101 in decimal, so the setting changes the answer.

For written-out numbers rather than other bases, the number to words converter may be what you need.