Logic Gate Truth Tables

Logic gates are the building blocks of digital circuits, determining how inputs combine to produce outputs. Understanding their truth tables helps in analyzing and designing circuits, making it essential for grasping concepts in Electrical Circuits and Systems I.

1. AND gate truth table

   • Outputs true (1) only when 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:

     A	B	A AND B
     0	0	0
     0	1	0
     1	0	0
     1	1	1

2. OR gate truth table

   • Outputs true (1) when 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:

     A	B	A OR B
     0	0	0
     0	1	1
     1	0	1
     1	1	1

3. NOT gate truth table

   • Outputs the inverse of the input; true (1) becomes false (0) and vice versa.
   • Symbolically represented as ¬A or NOT A.
   • Essential for creating complementary signals in circuits.
   • Truth table:

     A	NOT A
     0	1
     1	0

4. NAND gate truth table

   • Outputs false (0) only when both inputs are true (1); otherwise, it outputs true (1).
   • Symbolically represented as A ↑ B or A NAND B.
   • Acts as a universal gate, meaning it can be used to create any other gate.
   • Truth table:

     A	B	A NAND B
     0	0	1
     0	1	1
     1	0	1
     1	1	0

5. NOR gate truth table

   • Outputs true (1) only when both inputs are false (0).
   • Symbolically represented as A ↓ B or A NOR B.
   • Also a universal gate, capable of creating any other logic gate.
   • Truth table:

     A	B	A NOR B
     0	0	1
     0	1	0
     1	0	0
     1	1	0

6. XOR gate truth table

   • Outputs true (1) when the inputs are different; false (0) when they are the same.
   • Symbolically represented as A ⊕ B or A XOR B.
   • Commonly used in applications requiring equality checks or parity bits.
   • Truth table:

     A	B	A XOR B
     0	0	0
     0	1	1
     1	0	1
     1	1	0

7. XNOR gate truth table

   • Outputs true (1) when the inputs are the same; false (0) when they are different.
   • Symbolically represented as A ⊙ B or A XNOR B.
   • Useful for applications requiring equality checks, such as error detection.
   • Truth table:

     A	B	A XNOR B
     0	0	1
     0	1	0
     1	0	0
     1	1	1