Base 2, or binary, represents numbers using only digits 0 and 1. Each column is a power of two instead of a power of ten. It is the native language of digital circuits and computer hardware.

Binary Calculator — binary arithmetic solver

Calculate Binary

Result

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Enter values and press Calculate.

How to Use This Binary Calculator

Binary arithmetic looks intimidating until you realize it is decimal addition with only two digits—but carry at 2 instead of 10, and borrow 2 instead of 10. I have watched CS students lose points on homework because they skipped the decimal checkpoint step. This calculator accepts two binary operands, runs your chosen operation, and prints conversion steps so you can trace where each bit came from.

Enter Binary Number A and B. Use digits 0 and 1 only; a binary point is allowed (for example 10.1).
Select an operation—addition, subtraction, multiplication, or division. For division, B must be non-zero.
Press Calculate. The result appears in binary with a decimal equivalent underneath for sanity-checking.
Review step-by-step output. Each stage shows decimal conversion, the arithmetic, and conversion back to binary—including fractional parts when needed.

Binary Formulas and Practical Applications

Binary is base 2—imagine counting with only "off" and "on" switches instead of ten finger symbols. Every column is a power of two, which is why memory sizes and subnet masks show up in binary-heavy forms.

Binary to decimal (integer part)

Value = Σ (digit × 2^position)

Example: 1101₂ = 1×2³ + 1×2² + 0×2¹ + 1×2⁰ = 13₁₀. Positions count from 0 at the rightmost bit.

Fractional binary

Fraction = Σ (digit × 2^−k)

Digits right of the binary point use negative exponents: 10.1₂ = 2 + 0.5 = 2.5₁₀. Not every decimal fraction has a finite binary expansion—another reason the step panel shows both forms.

Addition carry rules

0+0=0, 0+1=1, 1+1=10₂ (write 0, carry 1). Three ones sum to 11₂. Subtraction borrows 2 from the next column—same idea as base ten, smaller base. For decimal-first work on large values, see the Big Number Calculator or explore all math calculators.

Standard Units and Conversion Tables

Quick binary–decimal reference for small integers common in intro courses:

Binary	Decimal
1010	10
1101	13
1111	15
10000	16
10.1	2.5

Frequently Asked Questions

How does binary calculation work?

Operands convert to decimal, the operation runs in decimal for accuracy, and the answer converts back to binary. Step text shows each conversion so you can follow the path on paper.

Can this calculator handle binary division with fractions?

Yes. Non-integer quotients display as binary fractions—for example 10.1₂ equals 2.5 decimal.

What is base 2?

A number system with digits 0 and 1 only. Each place value is a power of two—the foundation of how processors store and move data.

How do you convert binary to decimal?

Multiply each bit by two raised to its column index and add. The step-by-step section expands this for your specific inputs.

Can I use a binary point for fractional values?

Yes. Enter values like 11.01 using 0 and 1 only; fractional bits use negative powers of two.

Disclaimer. RapidRatio is informational only—not engineering or certification advice. Verify conversion steps for critical academic or hardware projects.