Universal Gate ppt to design digital logic circuit

Universal Gate ppt.ppt

1. •Universal Gate –NAND & NOR

2. Universal Gate –NAND
This presentation will demonstrate
•The basic function of the NANDgate.
•How a NANDgate can be used to replace an ANDgate,
an ORgate, or an INVERTERgate.
•How a logic circuit implemented with AOIlogic gates can
be re-implemented using only NANDgates.
•That using a single gate type, in this case NAND, will
reduce the number of integrated circuits (IC) required to
implement a logic circuit.
AOI Logic NAND Logic
More ICs = More $$Less ICs = Less $$

3. NAND Gate
XYZ
001
011
101
110
X
YY X YXZ 

4. NAND Gate as an Inverter Gate
XZ
01
10
XXZ XXX
(Before Bubble)
Equivalent to Inverter

5. NAND Gate as an AND Gate
XYZ
000
010
100
111
X
Y YX YXZ  YX
NAND Gate Inverter
Equivalent to AND Gate

6. NAND Gate as an OR Gate
XYZ
000
011
101
111
Equivalent to OR Gate
X
YYXY X Y XZ  X
NAND Gate
InvertersY

7. NANDGate Equivalent to AOIGates
INVERTERORAND

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

9. NAND Implementation
Example:
Design a NAND Logic Circuit that is equivalent to the AOI circuit
shown below.CA C B 

10. NAND Implementation
Solution –Step 2
Identify and replace every AND,OR, and INVERTER gate with its
NAND equivalent.

11. NAND Implementation
Redraw the circuit.
Solution –Step 3

12. NAND Implementation
Identify and eliminate any double inversions.
Solution –Step 4

13. NAND Implementation
Solution –Step 5
Redraw the circuit.

14. Proof of EquivalenceC C B C A C A C BZ
C AC BZ
CA C B




15. AOI vs. NAND
ICType Gates Gate / IC# ICs
74LS04 1 6 1
74LS08 2 4 1
74LS32 1 4 1
TotalNumber of ICs → 3
ICType Gates Gate / IC# ICs
74LS00 4 4 1
TotalNumber of ICs → 1

16. Universal Gate –NOR
This presentation will demonstrate…
•The basic function of the NORgate.
•How an NORgate can be using to replace an ANDgate,
an ORgate or an INVERTERgate.
•How a logic circuit implemented with AOIlogic gates
could be re-implemented using only NORgates
•That using a single gate type, in this case NOR, will
reduce the number of integrated circuits (IC) required to
implement a logic circuit.
AOI Logic NOR Logic
More ICs = More $$Less ICs = Less $$

17. NOR Gate
XYZ
001
010
100
110
X
YY X Y XZ 

18. NOR Gate as an Inverter Gate
XZ
01
10
XXZ XXX 
(Before Bubble)
Equivalent to Inverter

19. NOR Gate as an OR Gate
XYZ
000
011
101
111
X
YYX Y XZ  Y X
NOR Gate “Inverter”
Equivalent to OR Gate

20. NOR Gate as an AND Gate
XYZ
000
010
100
111
Equivalent to AND Gate
X
YY XY X Y XZ  X
NOR Gate
“Inverters”Y

21. NORGate Equivalent of AOIGates
INVERTERORAND

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

23. NOR Implementation
Example:
Design a NOR Logic Circuit that is equivalent to the AOI circuit
shown below.CA C B 

24. NOR Implementation
Solution –Step 2
Identify and replace every AND,OR, and INVERTER gate with its
NAND equivalent.

25. NOR Implementation
Redraw Circuit.
Solution –Step 3

26. NOR Implementation
Identify and eliminate any double inversions.
Solution –Step 4

27. NOR Implementation
Solution –Step 5
Redraw Circuit.

28. Proof of EquivalenceB CA C AC A  C A C BZ
C A C B

 C C A C BC BCB  C A C B

29. AOI vs NOR
ICType Gates Gate / IC# ICs
74LS04 1 6 1
74LS08 2 4 1
74LS32 1 4 1
TotalNumber of ICs → 3
ICType Gates Gate / IC# ICs
74LS02 7 4 2
TotalNumber of ICs → 2