Softonic

Number Base Converter

Step 1 / 2
Results

Enter a number in any base from 2 to 36 and this converter shows the equivalent in every other common base, binary, octal, decimal and hexadecimal, plus custom bases up to 36 where digits extend through the alphabet. It handles signed integers and, optionally, fractional parts for exact cross-base representation.

How the converter works

  1. 1

    Pick the source base

    Tell the tool what base your input number is written in.

  2. 2

    Type the value

    Use 0-9 for bases up to 10, A-Z for digits 10-35.

  3. 3

    Read all target bases

    The tool converts to binary, octal, decimal, hex and any custom base you pick.

  4. 4

    See the steps

    Each positional digit is broken down so you can verify or teach the conversion.

Common bases and their digits

Base Name Digits used
2 Binary 0, 1
8 Octal 0-7
10 Decimal 0-9
16 Hexadecimal 0-9, A-F
32 Base32 0-9, A-V (RFC 4648)
36 Alphanumeric 0-9, A-Z

Conversion by positional expansion

The number 1A3 in base 16 equals:

1 · 16² + 10 · 16¹ + 3 · 16⁰ = 256 + 160 + 3 = 419₁₀

Going the other direction, repeatedly divide by the target base and collect remainders:

419 / 16 = 26 remainder 3
 26 / 16 = 1  remainder 10 (A)
  1 / 16 = 0  remainder 1

Read remainders bottom to top: 1A3.

Quick reference for programmers

  • Binary to hex: group bits in fours from the right. 11010110 → D6.
  • Binary to octal: group bits in threes from the right. 11010110 → 326.
  • Hex to binary: each hex digit becomes exactly four bits.
  • Signed integers: most conversions assume unsigned. For two’s complement, the bit width matters, 0xFF is 255 unsigned but -1 as an 8-bit signed int.

Bases for obscure reasons

  • Base 12 (duodecimal) has been proposed for human counting because 12 factors cleanly.
  • Base 20 (vigesimal) underlies Mayan and Yoruba numerals.
  • Base 60 (sexagesimal) survives in time and angle measurement, inherited from Babylonian maths.

Frequently Asked Questions

Base 36 is the largest common base that uses only digits 0-9 and letters A-Z without needing case sensitivity. Base 62 extends by using uppercase and lowercase separately, but it is much less standardised.

Yes, as signed values with a minus sign. For bitwise two’s complement representations (relevant to programming), you need to specify the bit width because the same decimal -1 maps to 0xFF (8-bit), 0xFFFF (16-bit) or 0xFFFFFFFF (32-bit).

Yes, but be warned: 0.1 in decimal is a repeating fraction in binary (0.00011001100…), which is why floating-point arithmetic often has tiny errors. The tool shows the fraction to a chosen number of digits.

A binary-to-text encoding, not a numeric base in the usual sense. It encodes three bytes (24 bits) as four ASCII characters from a 64-character alphabet. Useful for transmitting binary over text-only channels like email.

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