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Binary Calculator
Binary arithmetic and conversion
Conversions
How It Works
The binary system is a numerical system that functions virtually identically to the decimal number system but uses the number 2 as its base. It uses only the digits 0 and 1, and each digit is referred to as a bit.
The binary system is a numerical system that functions virtually identically to the decimal number system but uses the number 2 as its base. While the decimal system uses digits 0 through 9, the binary system uses only 0 and 1. Almost all modern technology and computers use the binary system due to its ease of implementation in digital circuitry using logic gates.
Converting from decimal to binary involves finding the largest power of 2 within the given number, subtracting that value, and repeating until no remainder remains. Converting from binary to decimal is simpler: determine all place values where 1 occurs and find the sum of those values.
Binary addition follows the same rules as decimal addition except carry-over occurs when the result equals 2 (rather than 10). Binary subtraction requires borrowing when 1 is subtracted from 0; the 0 in the borrowing column becomes 2. Binary multiplication is simpler than decimal since only 0 and 1 are used.
Results
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Quick Tips
- • Results update automatically as you type
- • Use Tab to navigate between fields
- • Press Enter to calculate