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’

DeMorgan's Theorem 1

DeMorgan's Theorem 1

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’

DeMorgan's Theorem 2

DeMorgan's Theorem 2

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.