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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