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NOT
Figure 12.10:
Realizing a NOT gate using a NAND gate

OR
The following statements are called DeMorgan's Theorems and can
be easily verified and extended for more than two variables.



(12.1) 



(12.2) 

(12.3) 

(12.4) 
In general: 
(12.5) 
Thus : 
(12.6) 
Now it is easy to see that
, which can be checked
from the truth table easily. The resulting realization of OR gate is
shown in 12.11
Figure 12.11:
Realization of OR gate by NAND gates

AND gate
Figure 12.12:
Realization of AND gate by NAND gates

XOR gate

(12.7) 
Clearly, this can be implemented using AND, NOT and OR gates, and
hence can be implemented using universal gates.
Figure 12.13:
XOR gate

XNOR gate

(12.8) 
Again, this can be implemented using AND, NOT and OR gates, and
hence can be implemented using universal gates, i.e., NAND or NOR gates.
Figure 12.14:
XNOR gate

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20070725