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Number Base Converter

The problem: Developers, CS students and hardware engineers constantly need to translate numbers between decimal, binary, hex and octal representations — a mental exercise that wastes time.

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Number Base Converter: the complete guide

A number base converter translates integers between the four numeral systems used in computing: decimal (base 10, human-readable), binary (base 2, CPU and memory representation), hexadecimal (base 16, memory addresses, color codes, bytecode), and octal (base 8, Unix file permissions, legacy systems). This tool also shows the two's complement representation for understanding how signed integers are stored in fixed-width registers, the ASCII character equivalent for values in the printable range, and a full 0-15 reference table.

When each base is used in real-world computing

Decimal is the base humans use for all everyday arithmetic. Binary is the base CPUs use internally — memory, registers, logic gates and network protocols all operate on bits. Hexadecimal is used everywhere binary data is displayed to humans: memory dump addresses (0x7FFFFFFF), color codes in CSS (#FF5733), byte representations in cryptographic hashes and file headers, and machine code disassembly. Octal appears primarily in Unix file permission masks (chmod 755 = binary 111 101 101) and some legacy network protocol fields.

Two's complement explained

Two's complement is how CPUs store signed integers in a fixed number of bits. For an 8-bit signed integer, values 0-127 are stored normally; negative numbers use the rule: flip all bits, then add 1. So -1 in 8-bit two's complement is 11111111. The advantage is that addition hardware works identically for both signed and unsigned numbers. This tool shows the two's complement representation using the minimum bit width needed for the value (8, 16, 32 or 64 bits).

Step by step: how to use Base Converter

  1. 1

    Type a number in the input field in its native base.

  2. 2

    Select the input base (Decimal, Binary, Hex, or Octal) using the buttons below the field.

  3. 3

    All four representations update instantly in the results grid.

  4. 4

    Click 'Use' on any result card to set that representation as the new input.

  5. 5

    Review the two's complement bit pattern and ASCII character at the bottom.

  6. 6

    Use the 0-15 reference table for quick lookup of common hex values.

Security & privacy

Number conversion is a pure mathematical operation performed entirely in your browser using JavaScript's BigInt type for arbitrary precision. No numbers are sent to any server. The tool works offline and is safe to use with sensitive values such as memory addresses, cryptographic key fragments or internal IDs.

Frequently asked questions