Working with different number systems? Our free binary converter instantly transforms numbers between binary, decimal, hexadecimal, and octal. Whether you're learning computer science, debugging code, working with digital electronics, or just curious about how computers represent numbers, this tool provides accurate conversions with explanations. Understand the relationships between number bases that power all modern computing.
Number base (or radix) refers to how many unique digits a number system uses. Binary (base-2) uses 0 and 1. Decimal (base-10) uses 0-9. Hexadecimal (base-16) uses 0-9 and A-F. Octal (base-8) uses 0-7. Computers natively use binary because electronic circuits have two states. Humans prefer decimal. Hexadecimal serves as a compact representation of binary that's easier for humans to read. Converting between bases is fundamental to computer programming, digital logic design, and understanding how computers work.
Our converter provides: Instant conversion between all major bases (2, 8, 10, 16). Support for very large numbers using BigInt. Signed and unsigned number representations. Binary grouping display (nibbles and bytes). Step-by-step conversion explanations. Copy-to-clipboard for any format. Mobile-friendly interface. No registration required. Works offline. Free unlimited conversions.
The converter uses mathematical algorithms to transform numbers between bases. For binary/hex/octal to decimal: It sums each digit multiplied by base^position. For decimal to other bases: It repeatedly divides by the target base and tracks remainders. For binary/hex/octal conversions: It uses the fact that 2³=8 and 2⁴=16, allowing direct digit grouping. BigInt handles arbitrarily large numbers beyond JavaScript's safe integer limit.
Programming - Converting memory addresses and color codes. Computer Science Education - Learning number systems. Digital Electronics - Working with logic circuits and binary data. Networking - Understanding IP addresses and subnet masks. Cryptography - Working with binary keys and hashes. Embedded Systems - Programming microcontrollers. Data Recovery - Interpreting raw binary data. Reverse Engineering - Analyzing binary files.
Our converter offers: Accuracy with precise mathematical algorithms. Speed with instant conversions. Education showing how conversions work. Convenience supporting all common bases. Large Number Support beyond typical limits. Accessibility on any device. No Cost completely free.
Computer Science Students learning number systems. Software Developers debugging binary data. Electrical Engineers working with digital logic. Network Administrators configuring subnets. Security Professionals analyzing binary protocols. Hobbyists exploring how computers work. Teachers demonstrating number base concepts.
Enter your number in any supported base. Select the input base if not auto-detected. View conversions to all other bases. Copy the format you need. Enter new numbers for additional conversions.
Verify Input Base is correctly selected. Use Hex for Compact representation of binary. Group Binary by 4 digits for easy hex reading. Check Signed/Unsigned if working with negative numbers. Understand Two's Complement for signed binary.
Very large numbers may display in scientific notation. Some edge cases with extremely large BigInt values. Browser-dependent precision for decimal fractions.
Binary is a base-2 number system using only digits 0 and 1. Computers use binary because electronic circuits have two states: on (1) and off (0). All computer data - numbers, text, images, programs - is ultimately stored and processed as binary. Understanding binary is fundamental to computer science and digital electronics.
To convert binary to decimal, multiply each digit by 2 raised to its position power (starting from 0 on the right), then sum the results. For example, 1011 binary = (1×2³) + (0×2²) + (1×2¹) + (1×2⁰) = 8 + 0 + 2 + 1 = 11 decimal. Our converter does this instantly for any binary number.
Hexadecimal (base-16) uses digits 0-9 and letters A-F. It's compact representation of binary - each hex digit represents exactly 4 binary digits (a nibble). This makes hex much shorter than binary for the same value. For example, binary 11111111 = FF hex = 255 decimal. Programmers use hex for memory addresses, color codes, and binary data.
Yes, our converter handles numbers up to JavaScript's safe integer limit (9,007,199,254,740,991) and beyond using BigInt for arbitrary precision. You can convert binary numbers with hundreds of digits. For extremely large numbers, the display may use scientific notation or truncate for readability, but the full precision is maintained internally.
Unsigned binary represents only positive numbers (0 to 2ⁿ-1). Signed binary can represent negative numbers using methods like two's complement. In two's complement (most common), the leftmost bit indicates sign (1 = negative). For example, 8-bit signed: 01111111 = +127, 10000000 = -128. Our converter supports both representations.
Different bases suit different purposes: Binary (base-2) is what computers use at the hardware level. Octal (base-8) was historically used for early computer systems (PDP-8, etc.). Hexadecimal (base-16) is compact and maps well to binary (4 bits per hex digit), making it ideal for memory addresses, colors, and binary data. Decimal (base-10) is what humans use naturally.
To convert decimal to binary: Divide the number by 2 and record the remainder (0 or 1). Continue dividing the quotient by 2 until you reach 0. The binary number is the remainders read in reverse order. For example, 13 decimal: 13÷2=6R1, 6÷2=3R0, 3÷2=1R1, 1÷2=0R1 → reading up: 1101 binary.
Binary prefixes use base-2: 1 KiB (kibibyte) = 1,024 bytes (2¹⁰), 1 MiB (mebibyte) = 1,048,576 bytes (2²⁰), 1 GiB (gibibyte) = 1,073,741,824 bytes (2³⁰). This differs from decimal prefixes (KB, MB, GB) which use base-10 (1,000; 1,000,000; etc.). Operating systems often display GiB but label it as GB, causing confusion about storage capacity.