Number System Converter Calculator
Convert between binary, octal, decimal, hexadecimal and any base from 2 to 36.
Convert a value between binary, octal, decimal and hexadecimal.
Inputs
- Value
- From base
What it does
Converts numbers between binary, octal, decimal, hexadecimal and any base from 2 to 36.
Where it's used
Reading datasheets and register maps, debugging firmware and coursework.
How to use it
- Type the value.
- Choose the base it is written in.
- Optional: pick another base for an extra conversion.
The formula explained
- N = Σ dᵢ·bⁱ
- each digit times the base to the power of its position
- Hex digit
- = 4 bits
- Octal digit
- = 3 bits
Worked example
Converting hex FF.
Inputs:
- Value: FF
- From base: Hexadecimal (16)
- Also convert to base: 36
The calculator gives:
- Decimal: 255
- Binary: 1111 1111
- Octal: 377
Tips and common mistakes
- In code,
0xmeans hex and0bmeans binary. - Bases above 10 use letters: A = 10 … Z = 35.
- Leading zeros do not change the value.
Questions people ask
How do I convert decimal to binary by hand?
Divide by 2 repeatedly and write down the remainders, then read them from last to first. 13 → 6 r1 → 3 r0 → 1 r1 → 0 r1, so 13 = 1101.
Why is hex so popular with programmers?
Each hex digit is exactly four bits, so binary converts digit by digit: 0x3F = 0011 1111. A byte is always two hex digits, which makes memory dumps and registers easy to read.
Where is octal still used?
Mainly in Unix file permissions, where each octal digit is three bits — read, write, execute. Permission 755 means rwx for the owner and r-x for everyone else.
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Enter your values to get the result with the formula, substituted values and an explanation of each step.