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Logic Gates

Logic Gates. The Inverter. The inverter (NOT circuit) performs the operation called inversion or complementation . Standard logic symbols:. 1. output. input. output. input. 1. Inverter Truth Table & Logic Expression. 1. 0. 0. 1. A. X = A. A. X. B.

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Logic Gates

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  1. Logic Gates

  2. The Inverter • The inverter (NOT circuit) performs the operation called inversion or complementation. • Standard logic symbols: 1 output input output input 1

  3. Inverter Truth Table & Logic Expression 1 0 0 1 A X = A

  4. A X B The AND Gate & Its Operation • The AND gate is composed of two or more inputs and a single output. • For a 2-input AND gate: • Output X is HIGH only when inputs A and B are HIGH • X is LOW when either A or B is LOW, or when both A and B are LOW. A & X B

  5. AND Gate Truth Table A X B • The total number of possible combinations of binary inputs to a gate is determined by: N = 2n • Therefore: • 2 bits (n=2) = 4 combinations • 3 bits = 8 combinations • 4 bits = 16 combinations

  6. AND Gate – Logic Expressions • Use either: • X = A · B ,or • X = AB • If there are more than 2 inputs, do as below: A X B A B X= ABC C A B X= ABCD C D

  7. ≥ 1 A X B The OR Gate • Like AND gate, an OR gate has two or more inputs and one output. • For a 2-input OR gate: • output X is HIGH when either input A or input B is HIGH, or when both A and B are HIGH. • X is LOW only when both A and B are LOW. A X B

  8. OR Gate Truth Table A X B

  9. OR Gate – Logic Expressions • Use the operator + for OR operation • X = A + B • If there are more than 2 inputs, do as below: A X= A+B+C B C A B X= A+B+C+D C D

  10. The NAND Gate • NAND = NOT-AND • For a 2-input NAND gate: • Output X is LOW only when inputs A and B are HIGH • X is HIGH when either A or B is LOW, or when both A and B are LOW A & A A X X X B B B

  11. NAND Gate Truth Table & Logic Expression A X B • The Boolean expression for the output of a 2-input NAND gate is X = AB

  12. Negative-OR Equivalent Op of a NAND • For a 2-input NAND gate performing a negative-OR operation • Output X is HIGH when either input A or input B is LOW or when both A and B are LOW NAND Negative-OR

  13. The NOR Gate • NOR = NOT-OR • For a 2-input NOR gate: • Output X is LOW when either input A or input B is HIGH, or when both A and B are HIGH • X is HIGH only when both A and B are LOW A ≥ 1 A A X X X B B B

  14. NOR Gate Truth Table & Logic Expression A X B • The Boolean expression for the output of a 2-input NOR gate is X = A+B

  15. Negative-AND Equivalent Op of a NOR • For a 2-input NOR gate performing a negative-AND operation • Output X is HIGH only when both inputs A and B are LOW NOR Negative-AND

  16. The XOR and XNOR Gates • Exclusive-OR and Exclusive-NOR gates are formed by a combination of other gates already discussed. • Because of their fundamental importance in many applications, these gates are often treated as basic logic elements with their own unique symbols.

  17. = 1 A X B The XOR Gate A • For a 2-input exclusive-OR gate: • Output X is HIGH when input A is LOW and input B is HIGH, or when input A is HIGH and input B is LOW • X is LOW when A and B are both HIGH and both LOW X B

  18. XOR Gate Truth Table & Logic Expression A X B • The Boolean expression for the output of a 2-input XOR gate is X = A+B

  19. = 1 A X B The XNOR Gate A • For a 2-input exclusive-NOR gate: • Output X is LOW when input A is LOW and input B is HIGH, or when input A is HIGH and input B is LOW • X is HIGH when A and B are both HIGH and both LOW X B

  20. XNOR Gate Truth Table & Logic Expression A X B • The Boolean expression for the output of a 2-input XNOR gate is X = A+B

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