1. What is Boolean Logic?

Boolean logic is a form of algebra where all values are reduced to either TRUE (1) or FALSE (0). It's the foundation of digital electronics and computer programming, used to make logical decisions based on input conditions.

2. How Does the Calculator Work?

The calculator implements the basic Boolean logic operations:

Where:

• \( variables \) — Input values (0 or 1)
• \( expr \) — Output result after applying the logic gate operation

3. Common Logic Gates

Basic Gates:

• AND: Output is 1 only if all inputs are 1
• OR: Output is 1 if at least one input is 1
• NOT: Output is the inverse of the single input
• NAND: AND followed by NOT
• NOR: OR followed by NOT
• XOR: Output is 1 if inputs are different
• XNOR: Output is 1 if inputs are the same

4. Using the Calculator

Instructions: Select a logic gate type, provide input values (0 or 1), and click Calculate to see the output. NOT gate only requires one input.

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between NAND and AND gates?
A: NAND is the negation of AND. While AND outputs 1 only when all inputs are 1, NAND outputs 0 in that case and 1 otherwise.

Q2: Why is Boolean logic important?
A: It's the foundation of digital circuits and computer operations, used in everything from simple devices to complex processors.

Q3: Can I simulate circuits with this calculator?
A: This is a basic single-gate calculator. For circuit simulation, you'd need more specialized software.

Q4: What's the practical use of XOR?
A: XOR is commonly used in cryptography, error detection, and arithmetic operations like binary addition.

Q5: How many inputs can real logic gates have?
A: While we typically show 2-input gates, many gates can have multiple inputs, though practical implementations often have limits.