Convert numbers between binary, decimal, hexadecimal, and octal. Perform arithmetic operations in any number system.
Binary (base-2) uses only two digits, 0 and 1, because computer hardware fundamentally operates on transistors that are either in an "on" or "off" electrical state - there's no natural way for hardware to reliably represent ten distinct states the way decimal (base-10) requires, which is exactly why binary became the foundation of all digital computing rather than an arbitrary design choice. Every piece of data a computer processes - text, images, video, numbers - is ultimately represented as binary at the hardware level.
Computer science students and programmers convert between binary, decimal, and hexadecimal regularly when working with low-level programming, understanding memory addresses, working with bitwise operations, or debugging network protocols where data is often represented in binary or hex format for compactness.
In binary, each position represents a power of 2 (1, 2, 4, 8, 16, and so on) rather than a power of 10 like decimal - converting binary to decimal means adding up the value of each position where a 1 appears, which is the core mechanic behind manual binary-to-decimal conversion.
Binary is a base-2 number system using only 0 and 1. It's the fundamental language of computers, representing all data as sequences of bits. Each binary digit (bit) represents a power of 2.
Hexadecimal (base-16) is commonly used in computing to represent binary data in a more human-readable format. Each hex digit represents 4 binary digits (bits), making it useful for memory addresses, color codes, and more.
To convert: first convert to decimal, then from decimal to the target base. For example, to convert binary to hex, convert binary to decimal, then decimal to hex. Our calculator does this automatically for you.
Yes! Enter your numbers in their respective bases, select the operation, and the calculator will perform the calculation and show the result in all number systems. This is useful for computer science and digital electronics.
Binary: 0, 1. Octal: 0-7. Decimal: 0-9. Hexadecimal: 0-9 and A-F (or a-f). Hexadecimal letters represent values 10-15 respectively.
Computer hardware operates on transistors that are either on or off, which naturally maps to two states (0 and 1) rather than the ten states decimal would require.
Each binary digit represents a power of 2 based on its position - add up the value of each position where a 1 appears to get the decimal equivalent.
Binary uses only 0 and 1, while hexadecimal uses 16 symbols (0-9, A-F) - hex is often used as a more compact, readable representation of binary data.
