Number Base Converter

Type in any number base field (Binary, Octal, Decimal, Hexadecimal) to instantly convert the value across all other bases.

Binary (Base 2)
Octal (Base 8)
Decimal (Base 10)
Hexadecimal (Base 16)
Number Details
8-Bit Binary Representation 11101000
32-Bit Binary Representation 00000000 00000000 00000011 11101000
ASCII Character Equivalent N/A (Non-printable)

Understanding Binary, Octal, Decimal, & Hexadecimal

Modern computation is powered by numerical representation architectures. Decimal (base 10) is our default human notation based on 10 fingers. Computers use Binary (base 2) for state routing because logic gates are strictly high/low or true/false (0/1).

Positional Notation Formula
Decimal Value = Σ (digit × baseᵖᵒˢⁱᵗⁱᵒⁿ), positions counted right to left starting at 0

Hexadecimal and Octal Utilities

Hexadecimal (base 16) is a compact method to display binary data. Every single hex digit represents precisely 4 binary bits (nibble), meaning a byte (8 bits) can be mapped using only 2 hex characters (e.g. `FF` is `11111111`). Octal (base 8) represents exactly 3 bits, historically used in file permissions (like unix `chmod 755`).

Converting Between Binary, Octal, Decimal and Hexadecimal

Programmers frequently need to convert numbers between bases — binary for low-level bit manipulation, hexadecimal for memory addresses and color codes, octal for legacy Unix file permissions, and decimal for everyday reading. This tool shows all four representations of the same value simultaneously, so you don't have to convert step by step.

Each base's "bit depth" context matters in practice: a byte (8 bits) ranges from 0 to 255 in decimal, 00 to FF in hexadecimal, and 00000000 to 11111111 in binary — understanding these boundaries helps when debugging overflow issues or working with fixed-width data types.

  • Simultaneous Display: See binary, octal, decimal, and hexadecimal values for the same number at once.
  • Common Use Cases: Hex is standard for color codes and memory addresses; binary is used for bitwise operations and flags.
  • Bit-Depth Awareness: Knowing the byte/word size you're working with helps interpret overflow and truncation behavior.
Number Base FAQ

Frequently Asked Questions

Common questions about machine numbers and conversions.

Hexadecimal is extremely useful because it maps 1-to-1 with binary nibbles. Since 16 is 2^4, translating hex to binary does not require complex multiplication or division — each digit corresponds exactly to 4 bits.
An 8-bit value (one byte) can represent integers from 0 to 255. A 32-bit value (4 bytes) represents integers up to 4,294,967,295, commonly used for standard memory addressing and 32-bit computing.
Octal is a base-8 radix system. Because it uses 8 as its multiplier block, it only requires eight distinct digits: 0, 1, 2, 3, 4, 5, 6, and 7. The digit 8 or 9 is invalid in octal math.
ASCII (American Standard Code for Information Interchange) is a character encoding standard mapping numbers 0 to 127 to English characters and symbols (for instance, the number 65 represents the uppercase letter 'A').
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