# Free Number System Converter - Binary, Decimal, Hexadecimal, Octal & More 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. ### Number Input Sample Live Preview Enter Number _e.g. 255_ From Base To Base Convert Clear ### Conversion ResultsLive Binary (Base 2) - Octal (Base 8) - Decimal (Base 10) - Hexadecimal (Base 16) - Base 32 - Base 36 - Live Conversion Results as you type 6 Number Bases Binary to Base 36 One-Click Copy Copy any result 100% Private No data sent anywhere ### What Is a Number System Converter? 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 binary (base 2), octal (base 8), decimal (base 10), hexadecimal (base 16), base 32, and base 36. For example, decimal 255 is binary 11111111 and hexadecimal FF. Enter whole numbers only; a leading minus sign is supported but fixed-width two's-complement output is not. For encoded text rather than numeral bases, use the [Base64 encoder](https://www.toolcomb.com/base64-encoder). For binary-size units such as bytes and bits, see the [bytes and bits converter](https://www.toolcomb.com/bytes-bits-converter). 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. #### 💻 Binary (Base 2) **Digits:** 0, 1 Computer hardware, logic circuits, low-level programming, bitwise operations #### 🔢 Octal (Base 8) **Digits:** 0–7 Unix/Linux file permissions (chmod), legacy computing, assembly language #### 🧮 Decimal (Base 10) **Digits:** 0–9 Everyday mathematics, human-readable numbers, standard arithmetic #### 🎨 Hexadecimal (Base 16) **Digits:** 0–9, A–F HTML/CSS colors, memory addresses, debugging, network protocols, cryptography #### 🔐 Base 32 **Digits:** 0–9, A–V Encoding systems, TOTP authentication tokens, Base32 data encoding #### 🌐 Base 36 **Digits:** 0–9, A–Z URL shorteners, unique IDs, alphanumeric encoding, slug generation ### How to Use the Number Converter - Step by Step 1. 1 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. 2 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. 3 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. 4 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. 5 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. 6 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. ### Common Conversion Examples & Reference Table | 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 | Same bits represent −128 in 8-bit two's complement | | 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 | ### Why Different Number Systems Matter in Computing #### Binary in Computer Hardware 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 in Web & Programming 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). #### Octal in Unix/Linux Permissions 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 for Compact IDs 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. ### Frequently Asked Questions - Number Base Converter #### How do I convert decimal to binary? To convert a decimal integer to binary, repeatedly divide by 2 and read the remainders from bottom to top. For example, 13 becomes 1101. Enter 255 as decimal to see 11111111 in binary and FF in hexadecimal. The tool accepts up to 4,096 digits. #### How do I convert binary to hexadecimal? 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. #### What is hexadecimal used for in programming? 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. #### Why is 255 significant in computing? 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. #### Can this tool convert negative numbers? Yes. Enter a minus sign before the integer; the result keeps that sign. This is signed magnitude notation, not a fixed-width two's-complement representation. Fractions are not supported. #### What are Unix file permission numbers like 755 and 644? 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--). #### What's the difference between base 32 and base 64 encoding? This tool converts integer values to a positional base-32 numeral using digits 0–9 and A–V. Standard Base32 and Base64 encode bytes using specified alphabets and padding rules; they are different operations from integer base conversion. ## Related Tools Discover more free tools that might help with your next task. 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