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Number Systems

Number Base Converter — Binary, Octal, Decimal, Hex

Enter a number in binary, octal, decimal, or hexadecimal and see it converted into all four bases at the same time.

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📝 Enter a Value

📊 Result — All Four Bases

Enter a value to convert it into all bases
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Disclaimer: This tool performs standard mathematical calculations for educational and reference purposes. Always double-check results independently for graded coursework or production code.

What a Number Base Is

A number base (or "radix") is simply how many unique digit symbols a counting system uses before it rolls over into a new column. Decimal, the system most people use daily, is base 10 and uses ten symbols (0–9). Computers work natively in binary (base 2), using only 0 and 1, and programmers often use octal (base 8) or hexadecimal (base 16) as shorter, more readable stand-ins for long binary strings.

Valid Digits by Base

Worked Example

Convert the decimal number 255 into the other three bases.

  1. Binary: 255 = 11111111
  2. Octal: 255 = 377
  3. Hexadecimal: 255 = FF

Frequently Asked Questions

Binary only has two symbols to work with (0 and 1), compared to decimal's ten (0–9), so each binary digit carries far less information than each decimal digit. To represent the same value, binary needs roughly 3.3 times as many digits as decimal — which is exactly why computers group binary digits into hex or octal for a shorter, more readable form.
Each hexadecimal digit maps cleanly onto exactly four binary digits (a nibble), so converting between binary and hex is just a matter of grouping bits — no arithmetic required. That clean mapping makes hex a compact, human-friendly shorthand for the raw binary values computers actually use internally, which is why you see it in color codes, memory addresses, and error codes.
Binary only allows 0 and 1. Octal allows 0 through 7. Decimal allows 0 through 9. Hexadecimal allows 0 through 9 plus the letters A through F (or a through f), where A=10 through F=15. Entering a digit outside that range for the selected base — like a 2 while in binary mode — isn't a valid number in that base, so the calculator flags it instead of guessing.
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