Binary Calculator
Perform direct arithmetic on binary strings (base-2). Automatically converts inputs and outcomes across binary, decimal, and hexadecimal numeral representations.
Binary digits containing only 0 and 1 (e.g. 10110 = 22 decimal)
Arithmetic operation to apply
Binary digits containing only 0 and 1 (e.g. 101 = 5 decimal)
Resulting value expressed in base-2 binary notation
How to Use This Calculator
- Enter the first binary string using only 0 and 1.
- Select addition, subtraction, multiplication, or division.
- Enter the second binary string.
- Inspect binary output alongside decimal and hexadecimal conversions.
Formula & Calculation Methodology
Binary arithmetic uses powers of 2 (2⁰, 2¹, 2², 2³...). Addition generates a carry to the next higher power whenever the sum exceeds 1.
Worked Example
Adding 10110₂ (22) + 101₂ (5)
Multiplying 110₂ (6) × 11₂ (3)
Frequently Asked Questions
Why does computer hardware rely on binary?↓
Physical transistors have two stable electrical states: on (high voltage / 1) and off (low voltage / 0), making binary hardware circuits resilient against electrical noise.
How does binary division handle remainders?↓
This calculator evaluates integer floor division in binary, returning the quotient without fractional floating bits.
What occurs if I enter non-binary characters like 2 or A?↓
The input cleaner automatically sanitizes input by filtering out any characters that are not 0 or 1.
What is a limitation of unsigned binary arithmetic?↓
Negative results in pure binary require two’s complement representation for signed register storage in 8, 16, or 32-bit hardware.
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Source Citation & Disclaimer
Informational tool only; not licensed tax, legal, or financial advice.