Cajigal Andrew 11/30/03 Extra Credit CSCI 310
NAND and NOR Implementation NAND and NOR functions are attractive to implement with electronic circuits. For instance, the NAND gate is considered a universal gate because any Boolean function can be implemented using these gates. Both the NAND and the NOR gates are implemented according to Demorgan's theorem. For example, the following relationship below is valid through Demorgan's theorem and conversion to NAND logic is performed as follows.
x' + y'
=
(xy)'
x y
(invert-OR) x' + y' =
x y
(xy)'
The same methodology is performed to convert to NOR logic.
x'y'
=
(x + y + z)'
x y
x y
(invert-AND) x'y' =
(x + y + z)'
One way that a functions can be manipulated is through the method of double complementation. The two expressions below are equivalent.
(x')'(y')'
=
xy
The following gate implementations are therefore equivalent.
x y
x y
Using the Demorgan's and theorem double complementation, it is possible to design a logic diagram composed solely of NAND gates or NOR gates. For example, suppose a Boolean function, F = xy + x'y' + x'y + xy' is to be implemented using only NAND gates. Begin by implementing the logic diagram using basic AND and OR gates.
x y
x' y'
x' y
x y'
Use double complementation to obtain the desired invert-OR gate
x y
x' y'
x' y
x y'
The resulting invert-OR can then be converted into a NAND gate
x y
x' y'
x' y
x y'
We can also implement logic diagrams using only NOR ...