DeMorgan’s Theorem

DeMorgan’s Theorem:

Theorem 1:

Statement: “The complement of two or more variable ANDed is equivalent to the OR of the Complements of the individual variables.

(XY)’ = X’ + Y’

X	Y	(XY)’	X’+Y’
0	0	1	1
0	1	1	1
1	0	1	1
1	1	0	0

Explanation:

According to this theorem the result of the first NAND gate is equivalent to the result of the second Negative-OR gate when the X and Y is reversed and passed to the Negative-OR gate.

 

Theorem 2

Statement: “The complement of two or more variables ORed is equivalent to the AND of the complements of the individual variables”.

(X+Y)’=X’Y’

X	Y	(X+Y)’	X’Y’
0	0	1	1
0	1	0	0
1	0	0	0
1	1	0	0

Explanation:     

According to this theorem the result of the first NOR gate is equivalent to the result of the second Negative-AND gate when the X and Y is reversed and passed to the Negative-AND gate.