Binary Number Calculator Form
Enter one or two binary values, choose an operation, and review conversions, statistics, complements, shifts, and charted bit composition.
Example Data Table
| Number A | Operation | Number B / Shift | Binary Result | Decimal Result |
|---|---|---|---|---|
| 101101 | Add | 1101 | 111010 | 58 |
| 11110000 | AND | 10101010 | 10100000 | 160 |
| 100101 | Left Shift | 2 | 10010100 | 148 |
| 00101101 | Two's Complement | 8-bit view | 11010011 | 211 unsigned |
| 101010 | Divide | 11 | 1110 remainder 0 | 14 |
Formula Used
Binary addition: add each bit with carry, moving right to left.
Binary subtraction: subtract each bit with borrowing when the top bit is smaller.
Binary multiplication: sum shifted partial products for each 1 bit in the multiplier.
Binary division: apply long division to produce a quotient and remainder.
Bitwise logic: compare aligned bits one position at a time for AND, OR, XOR, NAND, NOR, or XNOR.
Left shift: A << n = A × 2n
Right shift: A >> n = floor(A ÷ 2n)
One's complement: invert every bit, so 0 → 1 and 1 → 0.
Two's complement: one's complement plus 1, commonly used for signed binary numbers.
Unsigned decimal conversion: sum each bit times its positional power of two.
Decimal = Σ(bit × 2position)
How to Use This Calculator
- Enter a valid binary value in Number A.
- Enter Number B when the selected operation needs a second operand.
- Choose the desired operation from the dropdown list.
- Enter a shift amount for left or right shift calculations.
- Set a word size for padding, complements, and signed interpretation.
- Press Calculate Binary Result.
- Review the result panel above the form, including conversions, parity, and chart.
- Use the CSV or PDF buttons to export the calculation summary.
Frequently Asked Questions
1. What does this binary number calculator do?
It performs binary arithmetic, bitwise logic, shifts, complements, comparison, and base conversions. It also shows parity, ones and zeros counts, a signed view, export options, and a Plotly chart.
2. Can I use very long binary numbers?
Yes. The calculator uses string-based processing for core binary math, so it is suitable for longer values than standard integer-only approaches. Extremely large inputs may still take longer to process.
3. What is the purpose of word size?
Word size controls padding and signed interpretation. It is especially useful for bitwise logic, one's complement, two's complement, and reading the result as a fixed-width binary value.
4. Why do shift operations change the value?
A left shift appends zeros and usually multiplies the value by powers of two. A right shift removes bits from the right side and usually divides the value by powers of two.
5. What is the difference between one's and two's complement?
One's complement flips every bit. Two's complement flips every bit and adds one. Two's complement is the common method for representing signed negative binary numbers in computing.
6. Why does subtraction sometimes show a negative result?
If Number B is greater than Number A, the subtraction result is negative. The calculator shows the binary magnitude with a minus sign and also provides the converted decimal value.
7. What does the parity output mean?
Parity shows whether the count of 1 bits in the result is even or odd. It is useful in digital systems, transmission checks, bit validation, and simple error-detection tasks.
8. What do the CSV and PDF buttons export?
They export the calculated summary shown in the result panel, including the selected operation, operands, binary result, conversions, bit statistics, and related calculation details.