How do I use the Binary Calculator?

Enter the required values, then calculate. The Binary Calculator shows results, formulas, and step-by-step work when available. No account is required.

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How it works

Binary uses bits 0 and 1 with place values that are powers of 2. Arithmetic uses the same column rules as decimal but carry/borrow happens at 2.

Σ bᵢ·2ⁱ · 1+1=10₂ (carry)

When to use

Use this tool when you need to: try binary addition 1010 + 101, or convert 10111₂ → 23 and 18₁₀ → 10010₂. Open Steps for column work.

How to use this tool

Enter your values in the fields above.
Review the formula and any mode options for your problem.
Read the result and the step-by-step solution.

Try binary addition 1010 + 101, or convert 10111₂ → 23 and 18₁₀ → 10010₂. Open Steps for column work.

Frequently asked questions

What is the Binary Calculator?: Binary uses bits 0 and 1 with place values that are powers of 2. Arithmetic uses the same column rules as decimal but carry/borrow happens at 2.
How do I use the Binary Calculator?: Enter the required values, then calculate. The Binary Calculator shows results, formulas, and step-by-step work when available. No account is required.
What formula does the Binary Calculator use?: Σ bᵢ·2ⁱ · 1+1=10₂ (carry)

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Binary calculator

Add, subtract, multiply, or divide two binary values — or convert binary ↔ decimal — with column-by-column steps like a physical binary worksheet.

How it works

What is binary?

The binary system works like decimal, but its base is 2 instead of 10. Digits are only 0 and 1 (bits). Modern computers use binary because circuitry can reliably detect two states — on and off — with simple logic gates.

Binary → decimal (place values)

Each bit multiplies a power of two. Rightmost is 2⁰ = 1, then 2, 4, 8, … Example: 10111₂ = (1×2⁴) + (0×2³) + (1×2²) + (1×2¹) + (1×2⁰) = 16 + 0 + 4 + 2 + 1 = 23₁₀.

Decimal → binary

Method A: find the largest power of 2 not greater than the number, subtract it, and repeat on the remainder (1-bits mark powers used). Method B: repeatedly divide by 2; remainders (read last→first) form the bits. Example: 18₁₀ → 10010₂.

Binary addition

Same idea as decimal addition, but when a column totals 2 you write 0 and carry 1 (because 2 = 10₂). Rules: 0+0=0, 0+1=1, 1+0=1, 1+1=10 (write 0, carry 1). Watch for 1+1 plus an existing carry.

Binary subtraction

Borrowing is needed only when subtracting 1 from 0. The borrowing column becomes “2” in binary terms (10₂), and a higher 1-bit is reduced by 1 — chained through runs of zeros if needed.

Binary multiplication

Like long multiplication: each 1-bit of the multiplier contributes a left-shifted copy of the multiplicand; 0-bits contribute nothing. Partial products are then added with binary addition.

Binary division

Binary long division mirrors decimal long division. Bring bits down one by one; when the running remainder is at least the divisor, subtract and write 1 in the quotient, otherwise write 0. This calculator also reports remainder.

Binary / decimal conversion table

Handy pairs used when learning binary place values:

Decimal	Binary
0	0
1	1
2	10
3	11
4	100
7	111
8	1000
10	1010
16	10000
20	10100

Related calculators

Hex groups four binary bits per digit — ideal after you leave pure bit strings. The basic calculator handles everyday decimal arithmetic.

How it works

Binary uses bits 0 and 1 with place values that are powers of 2. Arithmetic uses the same column rules as decimal but carry/borrow happens at 2.

Σ bᵢ·2ⁱ · 1+1=10₂ (carry)

When to use

Use this tool when you need to: try binary addition 1010 + 101, or convert 10111₂ → 23 and 18₁₀ → 10010₂. Open Steps for column work.

How to use this tool

Enter your values in the fields above.
Review the formula and any mode options for your problem.
Read the result and the step-by-step solution.

Try binary addition 1010 + 101, or convert 10111₂ → 23 and 18₁₀ → 10010₂. Open Steps for column work.

Frequently asked questions

What is the Binary Calculator?: Binary uses bits 0 and 1 with place values that are powers of 2. Arithmetic uses the same column rules as decimal but carry/borrow happens at 2.
How do I use the Binary Calculator?: Enter the required values, then calculate. The Binary Calculator shows results, formulas, and step-by-step work when available. No account is required.
What formula does the Binary Calculator use?: Σ bᵢ·2ⁱ · 1+1=10₂ (carry)

Browse categories

How it works

What is binary?

Binary → decimal (place values)

Each bit multiplies a power of two. Rightmost is 2⁰ = 1, then 2, 4, 8, … Example: 10111₂ = (1×2⁴) + (0×2³) + (1×2²) + (1×2¹) + (1×2⁰) = 16 + 0 + 4 + 2 + 1 = 23₁₀.

Decimal → binary

Binary addition

Same idea as decimal addition, but when a column totals 2 you write 0 and carry 1 (because 2 = 10₂). Rules: 0+0=0, 0+1=1, 1+0=1, 1+1=10 (write 0, carry 1). Watch for 1+1 plus an existing carry.

Binary subtraction

Borrowing is needed only when subtracting 1 from 0. The borrowing column becomes “2” in binary terms (10₂), and a higher 1-bit is reduced by 1 — chained through runs of zeros if needed.

Binary multiplication

Like long multiplication: each 1-bit of the multiplier contributes a left-shifted copy of the multiplicand; 0-bits contribute nothing. Partial products are then added with binary addition.

Binary division

Decimal

Binary

100

111

1000

1010

10000

10100