Number Base Converter

Local

Instantly convert between binary, octal, decimal, and hexadecimal. Visualize any number as 8, 16, 32, or 64-bit — all computed locally with BigInt precision.

BinaryBase-2
0-10b
OctalBase-8
0-70o
DecimalBase-10
0-9
HexadecimalBase-16
0-F0x
Bit Width
Quick Reference Table
DecimalOctalHexBinary
0000
1111
22210
33311
444100
555101
666110
777111
81081000
91191001
1012A1010
1113B1011
1214C1100
1315D1101
1416E1110
1517F1111
16201010000
324020100000
64100401000000
1282008010000000
255377FF11111111
256400100100000000

All conversions run locally · Supports integers up to JavaScript BigInt limits

The Four Number Systems Every Developer Uses

Modern computing uses four number bases constantly. Understanding their relationships is fundamental to low-level programming, debugging, networking, and hardware design.

Quick Reference

  • Binary (Base-2): CPU instructions, bitwise operations, boolean logic, network masks
  • Octal (Base-8): Unix file permissions (chmod 755 = rwxr-xr-x), some assembly dialects
  • Decimal (Base-10): Human-readable integers, counter values, port numbers
  • Hexadecimal (Base-16): Memory addresses, CSS colors, byte dumps, Unicode code points, MAC addresses

Number Base Converter FAQs

Each binary digit (bit) represents a power of 2. Multiply each bit by 2 raised to its position (from right, starting at 0) and sum the results. For example, binary 1010 = 1×8 + 0×4 + 1×2 + 0×1 = 10 in decimal.

Repeatedly divide the decimal number by 16 and record the remainders. Map remainders 10–15 to letters A–F. Read the remainders in reverse order. For example, 255 ÷ 16 = 15 remainder 15 (F), so 255 in hex is FF.

Octal (base-8) is commonly used in Unix file permissions (e.g. chmod 755) where each digit represents 3 bits: read (4), write (2), execute (1). It's also used in older computing systems and some embedded applications.

Hexadecimal is used everywhere in programming: memory addresses (0x7FFF), color values (#FF5733), byte representations, bitwise masks, Unicode code points (U+1F600), and network MAC addresses.

This tool uses JavaScript's BigInt, which can handle arbitrarily large integers. There is no fixed maximum — it can convert numbers with thousands of digits.

AI models perform approximate arithmetic and can hallucinate results, especially for large numbers or multi-step conversions. This tool uses JavaScript BigInt for exact, deterministic conversions every time.

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