Number Base Converter
LocalInstantly convert between binary, octal, decimal, and hexadecimal. Visualize any number as 8, 16, 32, or 64-bit — all computed locally with BigInt precision.
| Decimal | Octal | Hex | Binary |
|---|---|---|---|
| 0 | 0 | 0 | 0 |
| 1 | 1 | 1 | 1 |
| 2 | 2 | 2 | 10 |
| 3 | 3 | 3 | 11 |
| 4 | 4 | 4 | 100 |
| 5 | 5 | 5 | 101 |
| 6 | 6 | 6 | 110 |
| 7 | 7 | 7 | 111 |
| 8 | 10 | 8 | 1000 |
| 9 | 11 | 9 | 1001 |
| 10 | 12 | A | 1010 |
| 11 | 13 | B | 1011 |
| 12 | 14 | C | 1100 |
| 13 | 15 | D | 1101 |
| 14 | 16 | E | 1110 |
| 15 | 17 | F | 1111 |
| 16 | 20 | 10 | 10000 |
| 32 | 40 | 20 | 100000 |
| 64 | 100 | 40 | 1000000 |
| 128 | 200 | 80 | 10000000 |
| 255 | 377 | FF | 11111111 |
| 256 | 400 | 100 | 100000000 |
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.