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Karnaugh Map (K-Map)

2 Column CSS Layout - concise design

Karnaugh Map (K-Map):

One variable, two variable, three variable, four variable:

Representation of truth table on karnaugh map:

Plot k-map fot the expression:

Y = (A+ B+ C+`D) (A+`B+`C+ D) (A+ B+`C+`D) (`A+`B+ C+ D) (`A+`B+`C+ D)

Grouping 2 adjacent cell:

Y=`A`B`C D + A`B`C D

= `B`C D (`A + A ) {RULE `A + A=1}

= `B`C D

Y=`A`BC+`ABC+ABC

=`A`BC+ `ABC+ `ABC+ ABC

=`AC(`B+B)+BC(`A+A) {RULE A+A=A}

=`AC+BC

Grouping 4 adjacent cell:

Y=`AB`CD+ `ABCD+ AB`CD+ ABCD

=`ABD(`C+C) +ABD(`C+C)

=`ABD+ABD

=BD(`A+A)

=BD

Grouping 8 adjacent cell:

Reduce the following expression to its SOP?

Y=`A`B`CD+ `ABCD+ `ABCD+ `ABC`D+ AB`C`D+ AB`CD+ ABCD+ A`BCD?

Reduce the following expression to its POS?

Y=(A+B+`C) (A+`B+`C) (`A+`B+`C) (`A+B+C) (A+B+C)?

UNIT 2 COMBIATIONAL CIRCUIT

Review of Boolean Theorem

Introduction to combinational logic circuit

Representation of logic function

UNIT 2 Digital logic circuit

2 Column CSS Layout - concise design

Boolean Theorems:

DeMorgans Theorems

He suggest tha two teoream that forms an important part of Boolean algebra.

In the equation form

1 . `A`B = `A + `B

The complement of the product is equal to the sum of the complements.

A	B	`A`B	`A + `B
0	0	1	1
0	1	1	1
1	0	1	1
1	1	0	0

2 . `A + `B =`A`B

The complement of the sum is equal to the product of the complements.

A	B	A + `B	A`B
0	0	1	1
0	1	0	0
1	0	0	0
1	1	0	0

UNIT 2 COMBIATIONAL CIRCUIT

Review of Boolean Theorem

Introduction to combinational logic circuit

Representation of logic function

Multiplexer

2 Column CSS Layout - concise design

MULTIPLEXER:

It select one of the input, it route to the output is known as data selector.

There are 2*n input lines and n selection lines whose bit combination determine which input line is selected.

Multiplexer is many to one (many input but one output).

2:1 MULTIPLEXER:

D0 is applied as an input to one AND gate and D1 is applied as an input to another AND gate.

Enable input is applied to both the gate.

An inverted S is applied to second input to first AND gate.

Selection line S is connected tas second input to second AND gate.

Output of both the AND gates are connected as input to the OR gate.

4:1 MULTIPLEXER:

8:1 MULTIPLEXER:

Design 16:1 multiplexer using 4:1 multiplexer ?

Implement the given function using multiplexer ?

Application of MULTIPLEXER:

They can be used to implement combinational logic circuit.

They are use in time multiplexing system.

They are used in frequency multiplexing system.

They are used in A/D or D/A converters.

They are used in data acquisition system.

MULTIPLEXER IC’S:

IC number	Function
74150	16:1 MUX
74151	8:1 MUX
74153	Dual 4:1 MUX
74157	Quad 2-inp MUX

UNIT 2 COMBIATIONAL CIRCUIT

Review of Boolean Theorem

Introduction to combinational logic circuit

Representation of logic function