What are digital circuits and how do they relate to Boolean logic?

What are digital circuits and how do they relate to Boolean logic?

Digital circuits are electronic circuits that operate using discrete values, typically representing binary states (0 and 1). Boolean logic is the mathematical framework that underpins these circuits, allowing for operations like AND, OR, and NOT.

Can you explain how an AND gate works?

An AND gate is a basic digital logic gate that outputs true (1) only if all its inputs are true (1). For example, if both inputs are 1, the output is 1; if either input is 0, the output is 0.

What is the significance of truth tables in Boolean logic?

Truth tables are used to represent the output of a logic gate or circuit for every possible combination of inputs. They help in understanding how the circuit behaves and in designing complex circuits.

How do you simplify Boolean expressions?

Boolean expressions can be simplified using laws and theorems like De Morgan's Theorems, the Distributive Law, and the Consensus Theorem, which help reduce the number of terms and make the expression more efficient.