Generalized De Morgan

1
Generalized De Morgans Theorem

• Lecture L5.4
• Section 5.1

2
What kind of gate is this?
!X
X
X
Z

W
Z
Y
!Y
Y
X Y !X !Y W Z 0 0 0 1 1 0 1 1
3
What kind of gate is thisif 0 TRUE and 1
FALSE?
!X
X
X
Z

W
Z
Y
!Y
Y
0 TRUE T
X Y Z
X Y !X !Y W Z 0 0 0 1 1 0 1 1

4
What kind of gate is this?
!X
X
Z
X

W
Z
Y
!Y
Y
X Y !X !Y W Z 0 0 0 1 1 0 1 1
5
What kind of gate is thisif 0 TRUE and 1
FALSE?
!X
X
Z
X

W
Z
Y
!Y
Y
0 TRUE T
X Y Z
X Y !X !Y W Z 0 0 0 1 1 0 1 1

6
Generalized De Morgans Theorem

• NOT all variables
• Change to and to
• NOT the result
• --------------------------------------------
• F X Y X Z Y Z
• F !((!X !Y) (!X !Z) (!Y !Z))
• F !(!(X Y) !(X Z) !(Y Z))

7
F !(!(X Y) !(X Z) !(Y Z))
8
F !(!(X Y) !(X Z) !(Y Z))
NAND Gate
9
F X Y X Z Y Z
X
Y
X
F
Z
Y
Z
10
F !(!(X Y) !(X Z) !(Y Z))
NAND Gate