Basic Logic Gates By : Ashima Wadhwa Assistant Professor (giBS)

Digital Systems Digital vs. Analog Waveforms Analog: values vary over a broad range continuously Digital: only assumes discrete values

Algebra: variables, values, operations In Boolean algebra, the values are the symbols 0 and 1 If a logic statement is false, it has value 0 If a logic statement is true, it has value 1 Operations: AND, OR, NOT Boolean Algebra and Logical Operators

Logic Gates A computer carries out all operations internally by means of combination of signals passing through standard blocks of built in circuits known as logic gates. A Logic Gate is an electronic circuit that operates on one or more input signals to produce standard output signals.

Basic Logic Gates NOT, AND, and OR Gates NAND and NOR Gates Exclusive-OR (XOR) Gate Exclusive-NOR Gate

NOT Gate -- Inverter X Y

Y = ~X Y = !X Y = not X Y = X’ Y = X not(Y,X) NOT

X~X~~X = X X ~X ~~X

AND Gate AND X Y Z Z = X & Y X Y Z

X & Y X and Y X Y X * Y XY and(Z,X,Y) AND U V

OR Gate OR X Y Z Z = X | Y X Y Z

OR X | Y X # Y X or Y X + Y X V Y X U Y or(Z,X,Y)

Basic Logic Gates and Basic Digital Design NOT, AND, and OR Gates NAND and NOR Gates Exclusive-OR (XOR) Gate Exclusive-NOR Gate

NAND Gate NOT-AND X Y Z W = X & Y Z = ~W = ~(X & Y) X Y W Z W

NAND Gate NAND X Y Z X Y Z Z = ~(X & Y) nand(Z,X,Y)

NOR Gate NOT-OR X Y W = X | Y Z = ~W = ~(X | Y) X Y W Z Z W

NOR Gate NOR X Y Z X Y Z Z = ~(X | Y) nor(Z,X,Y)

Basic Logic Gates and Basic Digital Design NOT, AND, and OR Gates NAND and NOR Gates Exclusive-OR (XOR) Gate Exclusive-NOR Gate

Exclusive-OR Gate X Y Z XOR X Y Z Z = X ^ Y xor(Z,X,Y) AOB = ~A.B + A. ~B

XOR X ^ Y X $ Y Y xor(Z,X,Y)

Basic Logic Gates and Basic Digital Design NOT, AND, and OR Gates NAND and NOR Gates Exclusive-OR (XOR) Gate Exclusive-NOR Gate

X Y Z XNOR X Y Z Z = ~(X ^ Y) Z = X ~^ Y xnor(Z,X,Y) A O B=A.B + ~A.~B

XNOR X ~^ Y !(X $ Y) Y xnor(Z,X,Y)

Queries?