Add, subtract, multiply, and divide binary numbers. Convert between binary, decimal, hexadecimal, and octal number systems.
This tool converts numbers between binary (base 2), decimal (base 10), and other number systems, and can perform arithmetic directly on binary values. Binary is the foundational number system used internally by all digital computers.
Binary uses only two digits (0 and 1). To convert binary to decimal, multiply each digit by 2 raised to its position power and sum the results — for example, binary 1011 = (1×8) + (0×4) + (1×2) + (1×1) = 11 in decimal.
Enter a number in binary or decimal format, and the calculator converts between the two, or performs arithmetic operations (addition, subtraction, multiplication) directly on binary values.
Example 1: Binary 1010 converts to decimal 10.
Example 2: Decimal 25 converts to binary 11001.
Why do computers use binary instead of decimal? Binary maps directly onto the two electrical states (on/off, or high/low voltage) that digital circuits naturally use, making it the fundamental language of computer hardware.
What is a bit and a byte? A bit is a single binary digit (0 or 1), and a byte is a group of 8 bits, commonly used as the basic unit for measuring digital storage and data.
How is binary related to hexadecimal? Hexadecimal is often used as a more compact, human-readable shorthand for binary, since each hex digit corresponds exactly to 4 binary bits.
How does binary addition work? Binary addition follows similar carrying rules to decimal addition, but with only two digits: 0+0=0, 0+1=1, 1+1=10 (which carries a 1 to the next position), similar to how decimal addition carries at 10.
What is two's complement used for? Two's complement is a standard method computers use to represent negative binary numbers, allowing both addition and subtraction to be performed using the same binary addition circuitry.