Basic Logic Gates

Logic gates are the building blocks of digital circuits, performing basic operations like AND, OR, and NOT. Understanding these gates is key in Algebraic Logic, as they help create complex logical expressions and enable efficient circuit design.

1. AND gate

   • Outputs true (1) only if both inputs are true (1).
   • Symbolically represented as A · B or A AND B.
   • Commonly used in digital circuits to ensure multiple conditions are met.
   • Truth table shows that the output is false (0) for all combinations except when both inputs are true.
   • Fundamental in constructing more complex logical expressions.

2. OR gate

   • Outputs true (1) if at least one input is true (1).
   • Symbolically represented as A + B or A OR B.
   • Useful for scenarios where any condition being true is sufficient.
   • Truth table indicates that the output is false (0) only when both inputs are false (0).
   • Forms the basis for inclusive logical operations in circuits.

3. NOT gate

   • Outputs the inverse of the input; true (1) becomes false (0) and vice versa.
   • Symbolically represented as ¬A or NOT A.
   • Essential for negating conditions in logical expressions.
   • Truth table shows a single input and its corresponding inverted output.
   • Acts as a building block for creating more complex gates and circuits.

4. NAND gate

   • Outputs false (0) only if both inputs are true (1); otherwise, it outputs true (1).
   • Symbolically represented as (A · B)' or A NAND B.
   • Considered a universal gate because any logical function can be constructed using only NAND gates.
   • Truth table reveals that it is the negation of the AND gate.
   • Widely used in digital electronics for its versatility and efficiency.

5. NOR gate

   • Outputs true (1) only when both inputs are false (0); otherwise, it outputs false (0).
   • Symbolically represented as (A + B)' or A NOR B.
   • Also a universal gate, capable of creating any logical function using only NOR gates.
   • Truth table shows that it is the negation of the OR gate.
   • Important in simplifying circuit designs and reducing the number of components.

6. XOR gate

   • Outputs true (1) if exactly one of the inputs is true (1); outputs false (0) if both are the same.
   • Symbolically represented as A ⊕ B or A XOR B.
   • Commonly used in arithmetic operations and error detection circuits.
   • Truth table indicates that the output is true only for the combinations (1,0) and (0,1).
   • Plays a crucial role in digital systems requiring exclusive conditions.

7. XNOR gate

   • Outputs true (1) if both inputs are the same; outputs false (0) if they are different.
   • Symbolically represented as (A ⊕ B)' or A XNOR B.
   • Functions as the complement of the XOR gate, useful for equality checks.
   • Truth table shows that it outputs true for (0,0) and (1,1) combinations.
   • Important in applications where matching conditions are necessary, such as in digital comparators.