Binary Calculator
Perform arithmetic and bitwise operations on binary numbers
Only 0s and 1s are allowed.
Only 0s and 1s are allowed.
Binary Result
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Decimal Result
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Operation
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Frequently Asked Questions
How does binary addition work? +
Binary addition follows the same principles as decimal addition but with only two digits (0 and 1). The rules are: 0+0=0, 0+1=1, 1+0=1, and 1+1=10 (0 carry 1). When both digits and a carry are 1, the result is 11 (1 carry 1).
What are bitwise AND, OR, and XOR operations? +
Bitwise AND returns 1 only when both bits are 1. Bitwise OR returns 1 when at least one bit is 1. Bitwise XOR (exclusive OR) returns 1 only when the bits are different. These operations are applied to each pair of corresponding bits in the two numbers.
What is the NOT operation in binary? +
The NOT (complement) operation flips every bit in a binary number: each 0 becomes 1 and each 1 becomes 0. For example, NOT 1010 = 0101. This calculator applies NOT to the first input value only.
Can binary numbers be negative? +
This calculator works with unsigned binary numbers. If a subtraction result would be negative, the calculator will display the absolute value and indicate it is negative. In computer systems, negative binary numbers are typically represented using two's complement notation.
How do I convert binary to decimal? +
To convert binary to decimal, multiply each bit by 2 raised to its position (starting from 0 on the right). For example, binary 1011 = 1x8 + 0x4 + 1x2 + 1x1 = 11 in decimal. This calculator shows both binary and decimal results automatically.