1. Universal gates

2. Lecture objectives
At the end of the lecture the students should be able to
implement NOT, AND, and OR gate using NAND gates only.
implement NOT, AND, and OR gate using NOR gates only.
Implement any logic circuit using universal gates only.

3. Universal Gates
A universal gate can implement any Boolean function without need to use any other gate type (AOI).
AOI- AND-OR-Invert
The NAND and NOR gates are universal gates
In practice, this is advantageous since NAND and NOR gates are economical and easier to fabricate and are the basic gates used in all IC digital logic families.

4. The NAND Gate

5. Implementing NOT gate using NAND gates

6. Implementing AND using NAND gates

7. Implementing OR using NAND gates

8. NAND Gate Equivalent to AOI Gates

9. Process for NAND Implementation
If starting from a logic expression, implement the design with AOI logic.
In the AOI implementation, identify and replace every AND,OR, and INVERTER gate with its NAND equivalent.
Redraw the circuit.
Identify and eliminate any double inversions (i.e., back-to-back inverters).
Redraw the final circuit.

10. Design a NAND Logic Circuit that is equivalent to the Boolean expression.

11. Step 1: If starting from a logic expression, implement the design with AOI logic

12. Step2: In the AOI implementation, identify and replace every AND,OR, and INVERTER gate with its NAND equivalent

13. Step 3: Redraw the circuit

14. Step 4:Identify and eliminate any double inversions.

15. Step 5: Redraw the final circuit.

16. Practice questions
Use NAND gates to implement each expression

17. NOR Gate

18. NOR Gate as an Inverter

19. NOR Gate as an OR Gate

20. NOR Gate as an AND Gate

21. NOR Gate Equivalent of AOI Gates

22. Process for NOR Implementation
If starting from a logic expression, implement the design with AOI logic.
In the AOI implementation, identify and replace every AND,OR, and INVERTER gate with its NOR equivalent.
Redraw the circuit.
Identify and eliminate any double inversions. (i.e. back-to-back inverters)
Redraw the final circuit.

23. Design a NAND Logic Circuit that is equivalent to the Boolean expression.

24. Step 1: If starting from a logic expression, implement the design with AOI logic.

25. Step 2: In the AOI implementation, identify and replace every AND,OR, and INVERTER gate with its NOR equivalent

26. Step 3: Redraw the circuit.

27. Step4: Identify and eliminate any double inversions.

28. Step 5: Redraw the final circuit.

29. Equivalent Gates
A NAND gate is equivalent to an inverted-input OR gate.

30. An AND gate is equivalent to an inverted-input NOR gate.

31. A NOR gate is equivalent to an inverted-input AND gate.

32. An OR gate is equivalent to an inverted-input NAND gate.

35. Practice questions
Use NOR gates to implement each expression

36. Exercise 1 Given the following diagrams:
Determine the Boolean expression
Construct the truth table.
Determine the SOP.
Implement the circuit using NAND and NOR gates

40. Exercise 2 Given the Boolean expression F = XZ + Y’Z + X’YZ
Draw the logic diagram (AOI) for the circuit
Implement the circuit using NAND and NOR gates.