# Logic Gates

## Logic Gates

### Basics of Logic Gates

• Logic gates are the fundamental building blocks of digital circuits.
• They perform basic logical functions that are fundamental to digital circuits.
• The most common types of logic gates are AND, OR, NOT, NAND, NOR, XOR and XNOR.
• All other logic operations can be derived from these basic ones.

### AND Gate

• The AND gate produces an output of 1 only if all its inputs are 1.
• Otherwise, the output is 0.
• In other words, it performs the logical AND operation.

### OR Gate

• The OR gate produces an output of 1 if any of its inputs are 1.
• Otherwise, the output is 0.
• It performs the logical OR operation.

### NOT Gate

• The NOT gate, also known as an inverter, produces the inverse of its input.
• If the input is 1, the output is 0, and if the input is 0, the output is 1.
• It performs the logical NOT operation.

### NAND Gate

• The NAND gate is a combination of an AND gate and a NOT gate.
• It produces an output of 0 only if all its inputs are 1, otherwise the output is 1.
• It performs the logical NAND operation.

### NOR Gate

• The NOR gate is a combination of an OR gate and a NOT gate.
• It produces an output of 1 only if all its inputs are 0, otherwise the output is 0.
• It performs the logical NOR operation.

### XOR Gate

• The XOR (exclusive OR) gate produces an output of 1 if an odd number of inputs are 1, and 0 otherwise.
• It performs the logical exclusive OR operation.

### XNOR Gate

• The XNOR (exclusive NOR) gate is a combination of an XOR gate and a NOT gate.
• It produces an output of 1 if there is an even number of 1’s in the input and 0, otherwise.
• It performs the logical exclusive NOR operation.

### Usage of Logic Gates

• Logic gates are used in a wide variety of digital systems from simple systems like basic calculators and digital clocks to complex ones like microprocessors and computer memory units.
• They form the basis for solving complex logical and mathematical problems in digital systems.

### De Morgan’s Theorem

• De Morgan’s theorem presents a method for simplifying complex logic gates.
• The first rule is that the negation of a conjunction is equal to the disjunction of the negations (NOT (A AND B) = (NOT A) OR (NOT B)).
• The second rule is that the negation of a disjunction is equal to the conjunction of the negations (NOT (A OR B) = (NOT A) AND (NOT B)).
• De Morgan’s theorem plays a crucial role in Boolean algebra which is foundational for digital circuit design.