Number Base Converter
Number base converter for binary, octal, decimal and hexadecimal, with the place-value working shown alongside the answer instead of just the result.
Most used number tools
Hex to Decimal
With the place-value working shown digit by digit, not just the answer.
Binary to Decimal
Each bit's contribution, plus a powers-of-two table.
Decimal to Fraction
Exact fractions, and nearest tape-measure fractions.
Convert between all four bases
Enter digits valid for that base. Whole numbers only.
Every number base converter on this site
Reference table
| Decimal | Binary | Octal | Hex | Why it matters |
|---|---|---|---|---|
| 8 | 1000 | 10 | 8 | one octal digit |
| 10 | 1010 | 12 | A | |
| 15 | 1111 | 17 | F | one hex digit |
| 16 | 10000 | 20 | 10 | 2^4 |
| 64 | 1000000 | 100 | 40 | |
| 100 | 1100100 | 144 | 64 | |
| 128 | 10000000 | 200 | 80 | one byte's high bit |
| 255 | 11111111 | 377 | FF | largest 8-bit value |
| 256 | 100000000 | 400 | 100 | 2^8 |
| 1024 | 10000000000 | 2000 | 400 | 2^10 |
| 4095 | 111111111111 | 7777 | FFF | three hex digits |
| 65535 | 1111111111111111 | 177777 | FFFF | largest 16-bit value |
Why these four bases
Binary is how hardware stores values. Hexadecimal is the compact way to write binary, since one hex digit is exactly four bits and a byte is always two hex digits. Octal groups bits in threes and survives mainly in Unix file permissions. Decimal is what people read.
The place-value method is identical in all of them: each digit is multiplied by the base raised to the power of its position, counting from zero at the right. The hex and binary pages show that expansion step by step.
What this tool won't do
It handles non-negative whole numbers only. Fractional values in other bases and signed representations using two's complement are different problems, and a converter that silently guessed at them would be worse than one that says so. For decimal fractions, the decimal to fraction converter handles exact and nearest-fraction output.
Common questions
What is FF in decimal?
255. It is the largest value that fits in one byte as an unsigned number, which is why it turns up constantly in color codes and memory dumps.
Why is hexadecimal used instead of binary?
Because one hex digit maps to exactly four bits, so a byte is always two hex digits. It writes binary compactly without breaking byte alignment, which decimal can't do.
Where is octal still used?
Mainly Unix file permissions, where each digit encodes read, write and execute as three bits. Outside that it is largely historical.
Does this handle negative numbers?
No. It converts non-negative whole numbers only. Signed values use two's complement, where the leftmost bit carries the sign and the same bits mean something different.
Sources
- Base conversion is arithmetic rather than a measured conversion, so there is no external factor to cite. The place-value method shown is the standard positional-notation definition.