Convert numbers between binary, decimal, octal, hexadecimal, base 32, and base 36 instantly. Live preview, one-click copy, and full conversion table — free online number base converter.
Live Conversion
Results as you type
6 Number Bases
Binary to Base 36
One-Click Copy
Copy any result
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A number system converter (also called a number base converter or radix converter) is a tool that transforms numbers from one positional numeral system to another — for example, converting a decimal number to binary, or converting hexadecimal to decimal. This free online converter handles all the most commonly used number bases: binary (base 2), octal (base 8), decimal (base 10), hexadecimal (base 16), base 32, and base 36.
Every number system uses a specific radix (base) that determines how many unique digits are available and how place values are calculated. While humans use decimal (base 10) in everyday life, computers, programming languages, and digital systems rely heavily on binary and hexadecimal representations.
Digits: 0, 1
Computer hardware, logic circuits, low-level programming, bitwise operations
Digits: 0–7
Unix/Linux file permissions (chmod), legacy computing, assembly language
Digits: 0–9
Everyday mathematics, human-readable numbers, standard arithmetic
Digits: 0–9, A–F
HTML/CSS colors, memory addresses, debugging, network protocols, cryptography
Digits: 0–9, A–V
Encoding systems, TOTP authentication tokens, Base32 data encoding
Digits: 0–9, A–Z
URL shorteners, unique IDs, alphanumeric encoding, slug generation
1. Enter Your Number
Type the number you want to convert in the "Enter Number" field. Enter only valid digits for your selected input base — for example, binary only accepts 0 and 1, hexadecimal accepts 0–9 and A–F.
2. Select the Input Base
Choose the number base of your input from the "From Base" dropdown. Select Binary (Base 2) if your input is a binary number like 1010, Decimal (Base 10) for standard numbers, or Hexadecimal for hex values like FF.
3. Select the Target Base
Choose your target base from the "To Base" dropdown. The primary conversion result highlights this conversion prominently at the top of the results panel.
4. Enable Live Preview
Toggle "Live Preview" on to see all conversion results update in real-time as you type. This is ideal for quickly exploring different values. Turn it off for manual control with the Convert button.
5. View All Conversions
The results panel automatically shows your number converted to all six supported bases simultaneously — not just your selected target base. This gives you a complete conversion table in one view.
6. Copy Any Result
Click the copy button next to any result to copy it to your clipboard. This is useful when working with code and needing hex color values, binary constants, or memory addresses.
| Decimal | Binary | Octal | Hexadecimal | Common Use |
|---|---|---|---|---|
| 0 | 0 | 0 | 0 | Zero / null value |
| 1 | 1 | 1 | 1 | True / single bit set |
| 8 | 1000 | 10 | 8 | One byte nibble |
| 10 | 1010 | 12 | A | Decimal ten |
| 15 | 1111 | 17 | F | Single hex digit max |
| 16 | 10000 | 20 | 10 | One hex column |
| 32 | 100000 | 40 | 20 | ASCII space character |
| 64 | 1000000 | 100 | 40 | Common power of 2 |
| 127 | 1111111 | 177 | 7F | Max 7-bit value / ASCII max |
| 128 | 10000000 | 200 | 80 | Min 8-bit signed negative |
| 255 | 11111111 | 377 | FF | Max 8-bit value / 0xFF |
| 256 | 100000000 | 400 | 100 | One byte overflow |
| 1024 | 10000000000 | 2000 | 400 | 1 Kilobyte |
| 65535 | 1111111111111111 | 177777 | FFFF | Max 16-bit unsigned |
All digital computers at the hardware level operate exclusively in binary — transistors are either on (1) or off (0). Understanding binary helps programmers work with bitwise operators (&, |, ^, ~, <<, >>), understand boolean logic, and debug low-level code. Every high-level programming operation ultimately reduces to binary logic gates.
Hexadecimal is the most programmer-friendly representation of binary data because each hex digit maps exactly to 4 binary bits (a nibble). HTML/CSS colors (#FF5733), memory addresses (0x7FFE4A2B), and cryptographic hashes (SHA-256 output) are all expressed in hex. Two hex digits represent exactly one byte (8 bits).
Unix and Linux file permissions use octal numbers (chmod 755, chmod 644). Each octal digit represents three binary bits, neatly mapping to Read/Write/Execute permission triplets for Owner/Group/Other. Understanding octal is essential for Linux system administration and shell scripting.
Base 36 uses all 36 alphanumeric characters (0–9, A–Z) to create compact, human-readable identifiers. URL shorteners (bit.ly, t.co), order numbers, and unique IDs use base 36 encoding to represent large numbers in fewer characters — making URLs shorter and IDs easier to type and share.
To convert a decimal number to binary, repeatedly divide the number by 2 and record the remainders from bottom to top. For example, 13 ÷ 2 = 6 R1, 6 ÷ 2 = 3 R0, 3 ÷ 2 = 1 R1, 1 ÷ 2 = 0 R1 — reading remainders upward gives binary 1101. Our tool does this instantly for any size number. Try entering 255 in decimal to see FF in hexadecimal and 11111111 in binary.
Group binary digits into groups of 4 from the right, then convert each group to its hex equivalent. For example, binary 11111111 becomes 1111 1111 = F F = FF in hexadecimal. Each hex digit represents exactly 4 binary bits, making this conversion clean and reversible.
Hexadecimal is used for memory addresses, machine code representation, color values in web development (#RRGGBB), cryptographic hashes, network MAC addresses, and debugging. It's more compact than binary (one hex digit = 4 bits) while still mapping cleanly to the binary system computers use internally.
255 (decimal) = FF (hex) = 11111111 (binary) represents the maximum value of an 8-bit unsigned integer (one byte). It appears everywhere in computing: maximum RGB color channel values (0–255), IPv4 subnet masks (255.255.255.0), HTTP response codes, and single-byte data limits.
This tool currently converts positive integers only. For negative numbers in computing contexts, representations like two's complement (a standard binary encoding of negative integers) require separate handling. To convert a negative number, handle the sign separately and convert the absolute value.
Unix permissions in octal: 7 = 111 binary = Read+Write+Execute, 6 = 110 = Read+Write, 5 = 101 = Read+Execute, 4 = 100 = Read only. So chmod 755 means Owner gets 7 (rwx), Group gets 5 (r-x), Others get 5 (r-x). chmod 644 = Owner gets 6 (rw-), Group and Others get 4 (r--).
Base 32 uses 32 characters (0–9, A–V in our tool, or A–Z, 2–7 in RFC 4648) while Base 64 uses 64 characters including uppercase, lowercase, digits, and symbols. Base 32 produces larger output than Base 64 but uses only alphanumeric characters, making it safer for case-insensitive systems and TOTP authentication codes.
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