Number Base Converter
Convert numbers between binary, octal, decimal, hexadecimal, and any custom base up to 36.
🎛️ Convert to any custom base
🧠Show successive division steps
Show successive division steps
Converting decimal 1024 to Base 36 using successive division:
Final Result (reversed remainders): SG
Base Digits Reference Table
| Base System | Digits & Symbols Used |
|---|---|
| Base 2 (Binary) | 0, 1 |
| Base 8 (Octal) | 0, 1, 2, 3, 4, 5, 6, 7 |
| Base 10 (Decimal) | 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 |
| Base 16 (Hexadecimal) | 0-9, A, B, C, D, E, F |
| Base 36 (Max) | 0-9, A-Z |
Number Systems Guide
Understanding positional notations and computer mathematics.
Binary Foundations
Base 2 uses only two digits (0 and 1) to represent information in computer architectures and electrical voltages.
Compact Hex Notation
Hexadecimal (Base 16) condenses large binary strings into groups of 4 bits, used widely in color codes and memory indexes.
Positional Logic
Every number system represents values through positional symbols scaled by exponent powers of that system's base.
Frequently Asked Questions
What is the maximum base supported?
Can I convert fractions or decimals?
Are results case-sensitive?
Binary, Decimal, Hex: One Number, Four Outfits
The bases and where you meet them
The same quantity, written in the alphabet each domain prefers:
| Base | Digits | Habitat |
|---|---|---|
| Binary (2) | 0–1 | How hardware actually stores everything |
| Octal (8) | 0–7 | Unix file permissions (chmod 755) |
| Decimal (10) | 0–9 | Humans |
| Hexadecimal (16) | 0–9, A–F | Colors (#7c3aed), memory addresses, MAC addresses |
Why hex and binary are best friends
One hex digit is exactly four binary digits — F = 1111, 7 = 0111 — so hex is binary folded into quarters for readability. That's why low-level values everywhere ship as hex: #FF is the byte 11111111 (255), and a permission like 0x1F unpacks mentally digit by digit. Decimal has no such alignment, which is why 255 looks arbitrary while FF looks structural.
Where conversions come up
Reading a color's red channel (#7c = 124), decoding chmod permissions, IP and subnet work (the subnet calculator lives one layer up from this), debugging anything bitwise. For arithmetic in binary rather than conversion, the binary calculator operates directly, and historical numerals — a different base game entirely — convert in the Roman numeral converter.