NAND and NOR gate are used in the design of digital circuit .AND,OR,NOT, into equalent NAND and NOR logic diagrams. The AND invert consist of AND graphic symbol followed by a small circle .it Is also possible to represent a NAND gate by an OR graphic symbol preceded By a small circle in all the inputs . The symbol is know as invert OR
F=XYZX
Y
Z
AND- invert
XY
Z
F=XYZ
Invert OR
XY
Z
F=X+Y+ Z
X
Y
Z
F=X Y Z = ( X+Y+Z )_ _ _
Invert And
OR Invert
X X_
XX
_
X X_
Three graphic symbol of inverter
F=AB+CD+EThe Sum of products form with AND andOR gate
A B C D E
AB
CD
E
F=AB+CD+E
NAND NAND implementation
A B C D E E
F=AB+CD+E
_
The NAND function is so implemented ,that it can be easily converted to a Sum Of products form by using DeMorgans theorem
A B C D E
E_
AB
CD
F=AB.CD.E__ __ ________
F=AB+CD+E
F=(A+B) (C+D)
F
(A+B)
(C+D)
E
ABCDE
AA B C D E
(A+B)
(C+D)
E
F
F=(A+B) (C+D)
NOR -AND implementation
NOR-NOR implementation
A B C D E
(A+B)
(C+D)
E
F=(A+B) (C+D)E
A B C D E
F=AB+CD+E________
AB
CD
E
The two forms NAND-AND and AND-OR are equalent forms
And can be treated .Both perform the AND-OR-INVERT
AND-NOR
A B C D E
AB
CD
EF=AB.CD.E
__ __ _
F=AB+CD+E________
AND-NOR circuit
AB
CD
A B C D E __
__
E_
F
F=AB+CD+E________
The OR-NAND and NOR forms perform the OR-AND-INVERT funcation
F
(A+B)
(C+D)
E
ABCDE
F=(A+B).(C+D).E
A B C D E
F
F=(A+B)+(C+D)+E =(A+B).(C+D).E
_____ ____
OR-NANDOR-NAND
B
C
A
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