truth tables of all logic gates

3 min read 15-03-2025

Logic gates are the fundamental building blocks of digital circuits. They perform basic logical operations on one or more binary inputs to produce a single binary output. Understanding their behavior is crucial for anyone working with digital electronics or computer science. This article will provide a comprehensive overview of the truth tables for all common logic gates. We'll cover AND, OR, NOT, NAND, NOR, XOR, and XNOR gates, explaining their functionality and illustrating their behavior with clear truth tables.

What is a Truth Table?

A truth table is a mathematical table used in logic—specifically in Boolean algebra—which sets out the functional values of logical expressions on each of their functional arguments. In simpler terms, it systematically lists all possible combinations of input values and the corresponding output value for a given logic gate. This allows us to easily visualize and understand the gate's operation.

The Basic Logic Gates: AND, OR, and NOT

Let's start with the three fundamental logic gates:

1. AND Gate

The AND gate outputs a "1" (true) only when all its inputs are "1" (true). Otherwise, the output is "0" (false).

Input A	Input B	Output (A AND B)
0	0	0
0	1	0
1	0	0
1	1	1

2. OR Gate

The OR gate outputs a "1" (true) if at least one of its inputs is "1" (true). The output is "0" (false) only when all inputs are "0" (false).

Input A	Input B	Output (A OR B)
0	0	0
0	1	1
1	0	1
1	1	1

3. NOT Gate (Inverter)

The NOT gate is a unary operator (it takes only one input). It simply inverts the input: a "1" becomes a "0", and a "0" becomes a "1".

Input A	Output (NOT A)
0	1
1	0

Universal Gates: NAND, NOR

NAND and NOR gates are incredibly important because they are universal gates. This means you can build any other logic gate using only NAND gates, or only NOR gates.

4. NAND Gate

The NAND gate is the inverse of the AND gate. Its output is "0" only when all inputs are "1"; otherwise, the output is "1".

Input A	Input B	Output (A NAND B)
0	0	1
0	1	1
1	0	1
1	1	0

5. NOR Gate

The NOR gate is the inverse of the OR gate. Its output is "1" only when all inputs are "0"; otherwise, the output is "0".

Input A	Input B	Output (A NOR B)
0	0	1
0	1	0
1	0	0
1	1	0

Exclusive Gates: XOR and XNOR

These gates deal with exclusive conditions.

6. XOR Gate (Exclusive OR)

The XOR gate outputs "1" if exactly one of its inputs is "1". If both inputs are the same (both 0 or both 1), the output is "0".

Input A	Input B	Output (A XOR B)
0	0	0
0	1	1
1	0	1
1	1	0

7. XNOR Gate (Exclusive NOR)

The XNOR gate is the inverse of the XOR gate. It outputs "1" if both inputs are the same (both 0 or both 1), and "0" otherwise.

Input A	Input B	Output (A XNOR B)
0	0	1
0	1	0
1	0	0
1	1	1

Conclusion

Understanding truth tables is essential for analyzing and designing digital circuits. This guide provides a comprehensive overview of the truth tables for all major logic gates. By mastering these tables, you'll gain a solid foundation in digital logic and its applications. Remember to practice constructing and interpreting these tables to solidify your understanding. Further exploration into Boolean algebra and Karnaugh maps will enhance your ability to work with more complex logic circuits.