Binary Calculator
Add, subtract, multiply, divide and perform AND, OR or XOR on binary integers, with decimal and hexadecimal conversions and quotient/remainder support.
Enter your values
Change any assumption and calculate again to compare results.
What This Binary Calculator Calculates
The Binary Calculator accepts base-2 integers and performs arithmetic or bitwise operations without first requiring you to convert the operands manually. Results are shown in binary, decimal and hexadecimal so you can verify the same integer across three common number systems.
This is particularly useful for programming, networking, electronics and computer-science exercises. Addition, subtraction, multiplication and integer division behave like ordinary integer arithmetic. AND, OR and XOR operate on individual bits.
Formula and Calculation Method
Binary digits can only be 0 or 1. The calculator validates each operand before converting it to an arbitrary-precision integer. Arithmetic operations are then performed exactly with JavaScript BigInt. For integer division, the main result is the quotient and a separate supporting value shows the remainder.
Bitwise AND returns a 1 only where both operands contain a 1. OR returns a 1 where either operand contains a 1. XOR returns a 1 where exactly one operand contains a 1. Leading zeros do not change the numeric value and are removed from the normalized result.
How to Use This Calculator
- Enter the values requested in the calculator workspace and keep units consistent.
- Select Calculate. The arithmetic runs locally in your browser.
- Review the main answer together with the supporting figures and formula shown beside it.
- Change one assumption at a time when comparing scenarios so you can see which input is affecting the result.
- Use Copy Result, Save Result Image or Share Result when you need a record of the calculation.
The page is designed to show more than a single unexplained number. Supporting values make it easier to verify the arithmetic, compare results with a spreadsheet or textbook, and reproduce the calculation later. When a calculator uses a unit selector, the unit affects the calculation exactly as described in the method section rather than being treated as decoration.
Worked Example
101101₂ equals 45 in decimal and 1011₂ equals 11. Adding them gives 111000₂, which is 56 decimal and 38 hexadecimal.
Replace the example values with the measurements or numbers that apply to your own problem. The default values are present to make the calculator immediately testable and to show the expected input format.
How to Interpret the Result
The decimal and hexadecimal conversions help catch typing errors. If the binary output looks unfamiliar, compare the decimal value with the arithmetic you expected. For division, remember that this calculator performs integer division rather than a fractional binary expansion.
Bitwise operations are most meaningful when you think of the operands as bit patterns. Different applications may also impose a fixed word size such as 8, 16, 32 or 64 bits; this page does not add fixed-width padding unless you type the leading zeros yourself.
Common Search Questions About Binary Calculator
How do I calculate this result?
Enter the required values in the calculator above and select Calculate. The result is shown together with supporting values and the formula used, so the arithmetic can be checked instead of treated as a black box.
Can I use this calculator on a phone?
Yes. The v113 workspace is responsive, and on small screens the result opens in the current viewport after calculation.
Does OfficeCalculator.Net upload my inputs?
The arithmetic for this calculator runs locally in the browser. The page does not require an account to perform the calculation.
Important Limitations
Inputs are limited to unsigned binary integers up to 256 bits for practical browser use. Subtraction may produce a negative result. This page does not implement two’s-complement fixed-width arithmetic, binary floating-point or signed overflow rules.
Round only after the main calculation when practical. Rounding inputs too early can magnify small differences, especially in formulas that involve powers, roots, logarithms, repeated operations or unit conversions.
Privacy, Mobile Results and Practical Use
The calculator performs its arithmetic in the browser and does not require an account. Values entered into the form are used to generate the result shown on the page. On narrow screens the result panel opens in the current viewport after calculation, so the answer does not get lost below long explanatory content.
Use the calculator as a transparent planning and checking tool. For coursework, engineering work, financial records or any other situation where precision matters, keep the original source values and verify rounding conventions. A calculator can evaluate a formula correctly while still producing an inappropriate real-world answer if the wrong inputs, units or definitions are supplied.
Frequently Asked Questions
What digits are valid in binary?
Only 0 and 1 are valid binary digits.
What does XOR do?
XOR returns 1 for a bit position when the two input bits are different, and 0 when they are the same.
How is binary division handled?
The calculator performs integer division and reports both quotient and remainder.