Calculation result
Step-by-step working
Calculation history
| Time | Inputs | Mode | Product | Decimal |
|---|---|---|---|---|
| No saved calculations. | ||||
Formula used
Binary multiplication follows ordinary positional multiplication. Each multiplier bit produces a shifted partial product. Added partial products form the final binary product.
Binary Product = Multiplicand × Multiplier Binary Value = Σ(bit × 2^position) Binary Fraction Value = Σ(bit × 2^-position)
Fixed-point values use powers of two for scaling. Their fractional bit counts combine during multiplication. Rounding may reduce the stored result precision afterward.
How to use
- Enter the first and second binary values.
- Select unsigned, signed, or complement representation.
- Choose bit widths and optional fixed-point settings.
- Select a multiplication visualisation method.
- Press Calculate product to view every result.
- Copy, print, or export the completed calculation.
Raw-pattern mode treats every entered digit as stored data. Select a width matching the intended machine representation. Incorrect widths can change signed values and overflow behaviour.
Example data
| First binary | Second binary | Binary product | Decimal product |
|---|---|---|---|
101 | 11 | 1111 | 15 |
1010 | 110 | 111100 | 60 |
1111 | 10 | 11110 | 30 |
101.1 | 10 | 1011.0 | 11 |
Frequently asked questions
How does binary multiplication work?
Binary multiplication uses only zero and one. Each one copies and shifts the multiplicand. The shifted rows are then added together carefully.
Can this calculator multiply binary fractions?
Yes, binary points are accepted in either input. Fractional positions combine when the values are multiplied. Output precision can then be rounded or preserved.
What does raw-pattern mode do?
Raw-pattern mode interprets digits using the selected width. The leading bit can represent a negative sign. This is useful for machine-format binary calculations.
What is two's complement multiplication?
Two's complement stores signed integers using modular binary values. The leading bit contributes a negative positional weight. Hardware commonly uses this format for arithmetic operations.
How is overflow detected?
Overflow occurs when the result exceeds available storage. Signed and unsigned ranges use different limits. The calculator checks the selected result width automatically.
Why can the encoded result differ?
The mathematical product can need more available bits. Encoding may truncate values to the requested width. An overflow warning explains when information was lost.
What is Booth recoding?
Booth recoding groups multiplier transitions into signed operations. Consecutive ones can require fewer additions and subtractions. The cycle table shows each generated shifted term.
Can I export multiple calculations?
Yes, batch pairs can be processed together. The current result and batch table enter CSV exports. PDF export creates a readable calculation summary document.
Are very large binary numbers supported?
The calculator uses arbitrary-precision integer arithmetic in browsers. Extremely long step displays may become difficult to read. Maximum displayed cycles can therefore be limited manually.