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Binary Calculator

Perform binary arithmetic (add, subtract, multiply, divide) and convert between binary, decimal, hexadecimal, and octal.

Binary Arithmetic
Value 1
Operation
Value 2
Number Base Converter

Enter a value in any base to convert to all others:

Binary (base 2)
Octal (base 8)
Decimal (base 10)
Hexadecimal (base 16)
Result
Binary Result
10000
Decimal: 16
BaseValue

Binary Number System

Binary is base-2, using only 0 and 1. It is the fundamental language of computers and digital electronics. Each digit is a "bit" (binary digit).

Binary Arithmetic Rules

OperationExamples
Addition0+0=0, 0+1=1, 1+1=10 (carry), 1+1+1=11
SubtractionUse two's complement for negative numbers
AND1 AND 1 = 1; all others = 0
OR0 OR 0 = 0; all others = 1
XOR1 XOR 1 = 0; 0 XOR 1 = 1