Discussion: Multiplexers

EET 130– Digital Systems I

Combinational Logic Analysis

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Outline of the lecture

Implementing Combinational Logic

Boolean Expressions from Logic Circuits

Universal property of NAND and NOR gates

Combinational logic using NAND and NOR

Objective of the Lecture

 After successful completion of the lecture students

will be able to:  Analyze basic combinational logic circuits

 Write the Boolean output expressions for any combinational circuit

 Develop truth tables from the output expressions for a combinational

circuit

 Design combinational logic circuit for a given Boolean output

expression

 Simplify a combinational logic circuit to its minimum form

 Use NAND and NOR gates to implement any combinational logic

function

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Implementing Logic Circuits

 Implement the logic expression

using standard logic gates

A

B

C

A

B

A

B

D

ABC

AB

ABD

A.B.DB.AC.BA. 

A.B.DB.AC.BA. 

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Implementing Logic Circuits

 Implement the logic expression (A+B)(B+C)(A+B+C)

using standard logic gates

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Implementing Logic Circuits

 Draw a logic circuit to simulate the following Boolean function :-

F = A' + B' + C' + D'

A

C

D

F B

A

C

D

F B

A

C

D F

B

A

D

C F

B

Comment: A logic circuit to implement a particular Boolean function is NOT unique; or for a given Boolean function, different circuit formation may be used)

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Implementing Logic Circuits

 Form a logic circuit to simulate the following Boolean

functions:-

))(( ABBA ++=

BA⊕=

) ()( BAABG +=

) ()( BAABG +=

)()( ABBABABABBAAAB +++=+++=

) ()( BAAB += ))(( ABBA ++=

BA⊕=

Ex-NOR gate

Implementing Logic Circuits

Implementing Logic Circuits

Implementing Logic Circuits

Implementing Logic Circuits

Implementing Logic Circuits

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Boolean Expressions from Logic Circuits

 When a logic circuit is given, the Boolean

expression describing that logic circuit can

be obtained by combining the input

variables in accordance with the logic gate

functions.

 The procedure is best illustrated with the

examples that follow

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Boolean Expressions from Logic Circuits

 Obtain the logic function for the following logic circuit

Write the expression for each gate from left to right

A X F

Y

B

X = AB Y = A'B' F = X + Y

= AB + A'B'

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Boolean Expressions from Logic Circuits

 Obtain the logic function for the following logic circuit

A X

F

Y

B

X = A + B Y = A' + B' F = XY

= (A + B)(A' + B')

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Boolean Expressions from Logic Circuits

 Obtain the logic function for the following logic circuit

A

C

FB

X

Y

X = BC

Y = (X + A')'

= (BC + A')'

F = ABY

= AB(BC + A')'

Boolean Expressions from Logic Circuits

 Obtain the Boolean expression for the following circuit and

simplify the resulting expression using K-map

Boolean Expressions from Logic Circuits

Universality of NAND and NOR Gates

How combinations of NANDs or NORs are

used to create the three logic functions.

It is possible, however, to implement any logic expression using only

NAND gates and no other type of gate, as shown.

Universality of NAND and NOR Gates

How combinations of NANDs or NORs are

used to create the three logic functions.

NOR gates can be arranged to implement

any of the Boolean operations, as shown.

Alternate Logic-Gate Representations

 To convert a standard symbol to an alternate:

 Invert each input and output in standard symbols.

 Add an inversion bubble where there are none.

 Remove bubbles where they exist.

Alternate Logic-Gate Representations

Interpretation of the two NAND gate symbols.

Alternate Logic-Gate Representations

Interpretation of the two OR gate symbols.

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Summary

Review of K-map and Practice

Implementing Combinational Logic

Boolean Expressions from Logic Circuits

Universal property of NAND and NOR gates

Combinational logic using NAND and NOR