Add, subtract, multiply or divide two binary numbers with exact BigInt arithmetic – the addition mode traces every column and carry for your actual operands.
Show calculation steps
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Arithmetic where the bits live
Adding, subtracting, multiplying and dividing directly in binary keeps you in the notation your problem already uses — masks, registers, address maths — and skips two error-prone base conversions per operation. All four operations here are BigInt-exact at any operand length.
Addition mode traces every column and carry for your actual operands; every mode cross-checks in decimal so a misread bit cannot survive unnoticed.
Worked example
1011 + 110 col 1: 1+0 = 1 col 2: 1+1 = 0 carry 1 col 3: 0+1+1 = 0 carry 1 col 4: 1+0+1 = 0 carry 1 carry out → 1 Sum: 1 0001 (11 + 6 = 17 ✓)
| Column a+b+carry | Write | Carry |
|---|---|---|
| 0+0+0 | 0 | 0 |
| 0+1+0 | 1 | 0 |
| 1+1+0 | 0 | 1 |
| 1+1+1 | 1 | 1 |
Division returns two answers
Integer division yields quotient AND remainder — 100011 ÷ 101 is 111 remainder 0 — matching long division, hardware dividers and the % operator. Treating the remainder as part of the answer rather than an error is half of thinking in integer arithmetic.
Negative results, honestly
Subtracting a larger value produces a signed magnitude like −10, the mathematical answer. Fixed-width wraparound (what a register would show) is a representation question — explore it with the Two’s Complement Calculator, where 2ⁿ-modular behaviour is the point.
Privacy
All arithmetic executes in your browser; operands never leave the page.
How to use the Binary Calculator
- Enter the two binary numbers in their panels.
- Pick the operation – add, subtract, multiply or divide.
- Click "Calculate".
- Addition shows a column-by-column carry trace; every result carries a decimal cross-check.
Frequently asked questions
What operations does the calculator support?
All four basics on binary integers of any length: addition (with full carry trace), subtraction (negative results allowed), multiplication, and division returning quotient and remainder separately.
How does binary addition carry?
Per column: 0+0=0, 1+0=1, and 1+1 writes 0 carry 1 – because 2 is 10 in binary. 1+1+carry writes 1 carry 1. The trace lists each column of YOUR numbers, which is how the method is learned fastest.
Can results be negative?
Yes – subtracting a larger from a smaller yields a minus sign with the magnitude (mathematical convention). The fixed-width two's-complement wraparound a CPU would produce is a different question – explore it with the complement calculators.
Is there a size limit?
None in practice – BigInt arithmetic keeps 200-bit operands exact. No silent float rounding can occur at any size.
What is the decimal cross-check for?
Verification at a glance: the result line restates the computation in decimal (e.g. 11 + 6 = 17), so a slip in reading binary is caught immediately.
Why practice arithmetic IN binary at all?
It cements how ALUs work: carries are wires, and the addition trace is literally the ripple-carry adder's behaviour. Subnetting, bitmask design and assembly debugging all lean on this fluency.
Is the arithmetic done locally?
Yes – all computation is in-page JavaScript; operands are never transmitted.
