Lecture No. 7

1. Lecture No. 7 Computer Logic Design Logic Gates

2. NAND Gate • Contraction of NOT-AND • Standard logic symbol • Output is LOW only when all inputs are HIGH • Bubble indicates ACTIVE LOW output • Output level is opposite to that of the AND gate E

3. NAND Gate • The truth table for a two input NAND gate

4. NAND Gate • Timing diagram of NAND gate

5. NAND Gate • NAND gate application example • Device Failure Alarm System • When all the fans are working, the input to the NAND gate is 111 and the output is 0 • If any one of the fan stops working, the output of the NAND gate becomes 1, which activates the alarm

6. NAND Gate as Negative-OR • The truth table for a two input NAND gate looks awfully similar to an OR gate with the inputs inverted.

7. Bubble signifies ACTIVE LOW INPUT NAND Gate as Negative-OR

8. NAND Gate as a Universal Gate • NAND gate can be used to perform all the fundamental gate operations (NOT, AND, OR) • Universal NAND gate

9. NAND as NOT Gate Join all the input pins of the NAND gate together

10. NAND as AND Gate • Using NAND gate to perform the AND gate operation • Remember NAND is NOT-AND. What if we inverse this one more level? NOT-(NOT-AND) = AND • Accomplished by applying a NOT operation (implemented through NAND gate) to the output of the NAND gate

11. NAND as OR Gate • Using NAND gate to perform the OR gate operation • Can we form NOR gate as well?

12. NOR Gate • Contraction of NOT-OR • The standard logic symbol • Produces a LOW output when one or more of its input is HIGH • Bubble indicates ACTIVE LOW output • The output logic is opposite to that of the OR gate

13. NOR Gate • Truth table for a two input NOR gate

14. NOR Gate • Timing diagram of a NOR gate

15. NOR Gate as Negative-AND • The truth table for a two input NOR gate looks awfully similar to an AND gate with the inputs inverted.

16. Bubble signifies ACTIVE LOW INPUT NOR Gate as Negative-AND

17. NOR Gate as a Universal Gate • NOR gate can be used to perform all the fundamental gate operations (NOT, AND, OR) • Universal NOR gate

18. NOR as NOT Gate Join all the input pins of the NOR gate together

19. NOR as OR Gate • Using NOR gate to perform the OR gate operation • Remember NOR is NOT-OR. What if we inverse this one more level? NOT-(NOT-OR) = OR • Accomplished by applying a NOT operation (implemented through NOR gate) to the output of the NOR gate

20. NOR as AND Gate • Using NOR gate to perform the AND gate operation • Can we form NAND gate as well?

21. XOR Gate • Exclusive OR (XOR for short) • Standard logic symbol • This gate has only two inputs • Logical expression • The output is HIGH only when the two the inputs are at opposite logic level

22. XOR Gate • The truth table for XOR Gate

23. XOR Gate • Timing diagram of XOR gate

24. XNOR Gate • Exclusive-NOR (XNOR for short) • Standard logic symbol This gate has only two inputs • Logical expression • The output is LOW only when the two inputs are at opposite logic level

25. XNOR Gate • Truth table for XNOR gate

26. XNOR Gate • Timing diagram of XNOR gate

27. Summary of logic gates • Fundamental logic gates • AND • OR • NOT • Universal gates • NAND • NOR • Other gates • XOR • XNOR • Standard logic symbol • Logical/Boolean expression • Truth table • Application example