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

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 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.

💻 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

DecimalBinaryOctalHexadecimalCommon Use
0000Zero / null value
1111True / single bit set
81000108One byte nibble
10101012ADecimal ten
15111117FSingle hex digit max
16100002010One hex column
321000004020ASCII space character
64100000010040Common power of 2
12711111111777FMax 7-bit value / ASCII max
1281000000020080Min 8-bit signed negative
25511111111377FFMax 8-bit value / 0xFF
256100000000400100One byte overflow
10241000000000020004001 Kilobyte
655351111111111111111177777FFFFMax 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 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.

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?

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.

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?

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.