digital

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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