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Binary Calculator

Add, subtract, multiply, and divide binary numbers with instant base-2 math arithmetic. Free, private, and browser-based binary calculator.

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How to use Binary Calculator

  1. 1

    Enter your first binary number using 0s and 1s.

  2. 2

    Select the arithmetic operator (+, -, *, /).

  3. 3

    Enter your second binary number and click Calculate.

Capabilities

  • Direct base-2 arithmetic addition, subtraction, multiplication, and division
  • Real-time invalid digit detection enforcing binary notation
  • Private client-side calculation in your browser

How Binary Arithmetic & Base-2 Calculations Work

The binary number system (base 2) is the foundational language of digital computing. Unlike decimal (base 10) which uses ten digits (0 through 9), binary relies strictly on two electrical states represented as 0 and 1. Digital processors, logic gates, and low-level software perform all fundamental data processing via base-2 arithmetic.

The Four Fundamental Rules of Binary Addition
  • 0 + 0 = 0: Zero sum, no carry.
  • 0 + 1 = 1: One sum, no carry.
  • 1 + 0 = 1: One sum, no carry.
  • 1 + 1 = 10: Sum 0, carry 1 to the next higher power of two.
  • 1 + 1 + 1 = 11: Sum 1, carry 1 (when adding with an incoming carry).

Worked Binary Addition Example

  1010  (Decimal 10)

+ 1101  (Decimal 13)

------

= 10111  (Decimal 23)

Verification: 16 + 4 + 2 + 1 = 23 in base 10.

Need to Convert Between Binary and Decimal?

Translate base-2 strings into decimal numbers or vice versa instantly.

Binary to Dec
Privacy & Processing

This tool operates in a sandbox directly inside your web browser. All parsing, processing, and downloads are rendered locally. Your file size, metadata, and contents never cross the network. It works completely offline.

Frequently Asked Questions

How does binary addition work?

Binary addition follows four basic rules: 0 + 0 = 0; 0 + 1 = 1; 1 + 0 = 1; and 1 + 1 = 10 (which is 0 with a carry of 1 to the next higher bit column).

Can I perform subtraction, multiplication, and division on binary numbers?

Yes. The calculator supports addition (+), subtraction (-), multiplication (*), and integer division (/) directly on binary (base-2) values.

What happens if I enter an invalid digit like 2 or 8?

The tool validates input digits in real time. Because binary only permits digits 0 and 1, any other character will be flagged as an invalid base-2 input.

What is the maximum integer size supported?

Calculations use standard JavaScript safe integer precision (up to 53 bits or 9,007,199,254,740,991 in decimal), easily accommodating typical 8-bit, 16-bit, and 32-bit computer architecture calculations.

Is this binary calculator free and private?

Yes. Calculations run locally inside your browser memory with zero tracking and no server calls.

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