3.2 Logic Gates and Logic Circuits

Objective: Construct a logic circuit

This section focuses on the fundamental building blocks of digital systems: logic gates. We will explore the behavior of various logic gates and then learn how to combine them to create more complex logic circuits. Understanding logic gates is crucial for designing and analyzing digital circuits.

Logic Gates

Logic gates are electronic circuits that perform Boolean logic operations on one or more input signals to produce an output signal. The most common logic gates are:

• AND gate: The output is HIGH (1) only if all inputs are HIGH (1).
• OR gate: The output is HIGH (1) if at least one input is HIGH (1).
• NOT gate: The output is the logical inverse of the input. If the input is HIGH (1), the output is LOW (0), and vice versa.
• NAND gate: The output is the inverse of the AND gate. It is LOW (0) only if all inputs are HIGH (1).
• NOR gate: The output is the inverse of the OR gate. It is HIGH (1) only if all inputs are LOW (0).
• XOR gate: The output is HIGH (1) if the inputs are different. It is LOW (0) if the inputs are the same.
• XNOR gate: The output is the inverse of the XOR gate. It is HIGH (1) if the inputs are the same and LOW (0) if they are different.

Logic Gate Truth Tables

The truth table shows the output of a logic gate for all possible combinations of input values.

AND Gate Truth Table

Input A	Input B	Output
0	0	0
0	1	0
1	0	0
1	1	1

OR Gate Truth Table

Input A	Input B	Output
0	0	0
0	1	1
1	0	1
1	1	1

NOT Gate Truth Table

Input	Output
0	1
1	0

NAND Gate Truth Table

Input A	Input B	Output
0	0	1
0	1	1
1	0	1
1	1	0

NOR Gate Truth Table

Input A	Input B	Output
0	0	1
0	1	0
1	0	0
1	1	0

XOR Gate Truth Table

Input A	Input B	Output
0	0	0
0	1	1
1	0	1
1	1	0

XNOR Gate Truth Table

Input A	Input B	Output
0	0	1
0	1	0
1	0	0
1	1	1

Constructing Logic Circuits

Logic circuits are built by combining logic gates. The output of one gate can be connected to the input of another gate to create more complex functions. For example, a circuit can be designed to perform addition, subtraction, or comparison.

Consider a simple circuit that implements a two-input AND gate. This can be constructed using a single AND gate with inputs A and B.

More complex circuits can be built by cascading multiple logic gates. For instance, a half-adder circuit can be constructed using an XOR gate and an AND gate.

Further Exploration

This section provides a foundation for understanding logic gates and circuits. Further exploration can involve designing and analyzing more complex circuits, using logic minimization techniques, and learning about different types of combinational and sequential logic circuits.