AI Math Assistant
BetaAsk questions about your calculation results
3 free questions per session
AI provides general assistance. Always verify important calculations.
About This Calculator
Binary is the base-2 number system that forms the foundation of all digital computing, using only the digits 0 and 1. Every file, image, and program on your computer is ultimately stored as binary data. This calculator performs arithmetic operations and conversions between binary, decimal, octal, and hexadecimal, making it indispensable for programming and computer science studies.
Quick Tips
- 1 Each binary digit (bit) represents a power of 2 from right to left.
- 2 Shift left by one bit to multiply by 2; shift right to divide by 2.
- 3 Two's complement lets you represent negative numbers in binary arithmetic.
Example Calculation
Convert decimal 255 to binary and hexadecimal.
Binary: 11111111 | Hex: FF | Octal: 377 | All 8 bits set — max value for one byte
How Binary Arithmetic Works
Binary (base-2) arithmetic follows the same rules as decimal arithmetic but uses only two digits: 0 and 1. Binary addition carries over when the sum exceeds 1 (1+1=10 in binary). Subtraction, multiplication, and division work similarly. Computers perform all calculations in binary, making it fundamental to digital systems.
Number Base Conversions
This calculator converts results between four number systems: binary (base-2), decimal (base-10), hexadecimal (base-16), and octal (base-8). Hexadecimal is widely used in programming and color codes. Octal was historically important in computing. Understanding conversions between these bases is essential for programmers and engineers.
Frequently Asked Questions
Each binary digit represents a power of 2, starting from the right. For example, 1010 in binary = 1×8 + 0×4 + 1×2 + 0×1 = 10 in decimal. This calculator performs the conversion automatically and shows the result in decimal, hexadecimal, and octal.
Binary numbers should contain only 0s and 1s. If you enter digits other than 0 and 1, the calculator will attempt to parse the input as a binary string. Digits like 2-9 are not valid in binary and may produce unexpected results.
JavaScript handles integers up to 2^53 - 1 (about 9 quadrillion). This means binary numbers up to 53 digits long can be calculated accurately. For most practical purposes, this is more than sufficient.