Exclusive OR (XOR) Calculator
Use this ex or calculator to compute A XOR B instantly. It supports decimal, binary, and hexadecimal input and also shows OR and AND for comparison.
Note: This tool uses non-negative integers and JavaScript BigInt operations for precise bitwise results.
What is an ex or calculator?
An ex or calculator is a tool for computing the exclusive OR operation, written as XOR. In logic and computer science, XOR compares two bits and returns 1 only when the bits are different. If they are the same, the result is 0.
At a high level, XOR answers the question: “Are these two values different at this bit position?” That makes it useful in binary arithmetic, cryptography, data processing, hardware design, and debugging.
XOR logic in one minute
Truth table for one bit:
- 0 XOR 0 = 0
- 0 XOR 1 = 1
- 1 XOR 0 = 1
- 1 XOR 1 = 0
Rule: XOR outputs 1 when inputs are different.
How to use this calculator
1) Choose your input base
Select decimal, binary, or hexadecimal based on your data source. If you are working with low-level code, binary or hex can be more intuitive than decimal.
2) Enter two values
Type Value A and Value B. Keep them non-negative integers. The tool validates your input and shows a clear error if the format is incorrect.
3) Click “Calculate XOR”
You will get:
- XOR result in decimal, binary, and hex
- OR result for side-by-side comparison
- AND result for additional context
- A bit-by-bit breakdown table (for reasonably sized values)
Why XOR matters in practice
Data comparison and change detection
XOR is excellent for finding differences between two binary values. Where bits differ, XOR produces 1. This makes mismatch detection quick and visually obvious.
Simple encryption concept
In stream ciphers and one-time-pad style demonstrations, XOR is often used to combine plaintext with a key. Applying the same key again reverses the operation, because XOR is self-inverse:
- (A XOR B) XOR B = A
Bit toggling
Need to flip a specific bit in a register or flags variable? XOR with a mask is a standard approach. Bits with mask=1 are toggled, mask=0 stay unchanged.
XOR vs OR vs AND
These three operations are related but serve different goals:
- OR sets a bit to 1 if either input has 1.
- AND sets a bit to 1 only if both inputs are 1.
- XOR sets a bit to 1 only if inputs differ.
When troubleshooting bitmasks, seeing all three side by side helps you confirm your intent quickly.
Common mistakes and how to avoid them
Mixing number bases
Entering 1010 as decimal when you intended binary will produce a very different result. Always confirm the selected base before calculating.
Using signed values accidentally
Bitwise operations on signed numbers can be confusing due to two’s complement representation. For clarity, this tool focuses on non-negative integers.
Ignoring width assumptions
In many systems, bit width (8, 16, 32, 64) matters. If width is important in your project, pad binary values to a fixed length when interpreting results.
Quick examples
- Decimal: 12 XOR 10 = 6
- Binary: 1100 XOR 1010 = 0110
- Hex: 0x3F XOR 0x0A = 0x35
Final takeaway
A reliable ex or calculator saves time and prevents manual bit errors. Whether you are learning logic gates, debugging code, or working with masks, XOR is one of the most useful operations in technical work. Use the calculator above to check your values instantly and understand exactly what changes at each bit position.