Chapter 4_Combinational Logic Circuits

Lecture: DIGITAL SYSTEMS Chapter 4: Combinational Logic Circuits Nguyen Thanh Hai, PhD Faculty of Electrical & Electronic Engineering Combinational Logic Circuits University of Technical

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Lecture:

DIGITAL SYSTEMS

Chapter 4:

Combinational Logic Circuits

Nguyen Thanh Hai, PhD

Faculty of Electrical & Electronic Engineering

University of Technical Education

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-Two or more AND terms and ORed together

-Each AND term containing one or more variables but no

complemented sign covers more than one variable in a term.

Example 4.1: ABC or MN TD

-Two or more OR terms and ANDed together.

-Each OR term containing one or more variables

However, we can use Demorgan’s theorem to convert

between POS and SOP.

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P Q P

Q + =

(POS) Sums

of Product

D) B)(C

(SOP) Products

of Sum D

C B A

D) (C B) (A D) B)(C (A

= +

=

+ + +

= + +

Demorgan’s theorem

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Method 2: add an extra term

And from Eq (*)

z=A(B+C)

z=A(B+C) ABC

(*)

4.2 Algebraic Simplification

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9

4.3 Designing Combinational Logic Circuits

Y =

Truth table

A B

B

B A B A

Y = +

B A

4.3 Designing Combinational Logic Circuits

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1 Truth table

2 AND for each case

3 Sum-of-product expression

4 Simplify the expression

5 Implement the circuit

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Review questions

1 Write sum-of-products expression for a circuit with four inputs and an output that is to be HIGH only when input A is LOW at the same time that exactly two other inputs are LOW.

2 Implement the expression of question 1 using all four-input NAND gates How many are required?

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4.4 Karnaugh Map Method

C AB

+

= ABC C B A

C B A C B A X

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C B

C AB C B A X

=

+

=

C B

C B A C B A X

=

+

=

B A

BC A C B A X

=

+

=

C C B A ABC

BC A C B A X

= +

A

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K_Looping Groups of Four

A

B B A BA A B A

B B A BA A B

C D C D DC C D

C

A

X = C

X =

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2

Loop

ABD AC

D C B

C D

AB

A

{

) 15 , 11 ( ) 13 , 12 ( ) 7 , 6 ( )

B D BC D

B

A

X = 1 2 3 + 1 3 + 1 3 +

3 2 1 3

2 1 3 2 1 3 2 1

) 14 , 10 ( ) 9 , 8 ( ) 7 , 6 ( ) 5 , 1 ( Loop Loop Loop Loop

BD A D C B D BC D

B A

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Note: to be able to represent the various way

-Similar for many inputs

-Write mathematic expressions for the above K-maps

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Example 4.7:

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Example 4.7:

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Review questions

1 Use K mapping to obtain the expression of Example 4-7.

2 Use K mapping to obtain the expression of Example 4-8 This should emphasize the advantage of K mapping for expressions containing many terms.

3 Obtain the expression of Example 4-9 using a K map

4 What is a don’t-care condition?

Examples at P 142-143

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Design steps:

1 Based on requirements, one will determine input variables and the corresponding output functions.

2 Draw the truth table for the relation between inputs and outputs.

3 Write the output function (its output can be SOP or POS)

4 Simplify the function.

5 Draw the simplified circuit.

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Design of Integrated Circuits

The requirement is that the output of an integrated circuit is high if and only if all its inputs are high.

a Design the circuit with 3 inputs and 1 output.

b Simplify the circuit having the least total gates

c Re-design the circuit with using NAND gates with two inputs only.

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Example 4.8:

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Given an integrated circuit, in which there are 2 inputs (A,B), a control input C and1 one output Y.

a Design this circuit when the output C is low, data of

A will go through to Y; when the output C is high, data of B will go through Y.

b Simplify the circuit having the least total gates

c Re-design the circuit with using NOR gates with two inputs only.

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Review questions

1 Design a logic circuit with three inputs A, B, C and an

output that goes LOW only when A is HIGH while B and C are different.

2 Which logic gates produce a 1 output in the disable

state?

3 Which logic gates pass the inverse of the input signal

when they are enabled.

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4.7 Basic Characteristics of Digital ICs

TTL Family

-Bipolar ICs: using bipolar junction transistor (NPN and PNP)

-TTL: transistor-transistor logic

-Standard series: 74xxxxx -TTL has several subfamilies

or series to describe different functions such as gate type, related to frequency, power and certain applications

NOR gate

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Various series within the TTL logic Family

Schottky TTL 74S 74S 04 (Hex INVERTER)

Low-power Schottky TTL 74LS 74LS 04 (Hex INVERTER)

Advanced Schottky TTL 74AS 74AS 04 (Hex INVERTER)

Advanced Low-power

Schottky TTL 74ALS 74ALS 04 (Hex INVERTER)

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TTL logic Family ICs

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CMOS Family -Unipolar digital ICs: using CMOS

(N-channel and P-(N-channel MOSFETs) -CMOS: complementary metal-oxide semiconductor

-Standard series: 40xxxxx or 74xxxxx -CMOS has several subfamilies or series to describe different functions such as gate type, related to speed, performance depending in certain applications

-40xxxx is the oldest CMOS series with the same function similar to the TTL family

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Various series within the CMOS logic Family

Metal-gate CMOS 40 4001 (quad NOR gates)

Metal-gate, pin-compatible with TTL 74C 74C02 (quad NOR gates)

Metal-gate, pin-compatible with TTL,

Silicon-gate, high-speed , pin-compatible and

electrically compatible with TTL 74HCT 74AS02 (quad NOR gates) Advanced-performance CMOS, not pin-

compatible or electrically compatible with TTL 74AC 74ALS02 (quad NOR gates) Advanced-performance CMOS, not pin-

compatible with TTL, but electrically

compatible with TTL

74ACT 74ALS02 (quad NOR gates)

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CMOS logic Family ICs

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Power and Ground

-Power supply: dc power and ground

-Power supply pin: Vcc for TTL family and V DD

for CMOS family

Logic-Level Voltage Ranges

-TTL family: Vcc=+5V

-CMOS family: V DD from +3V to +18V Often use

+5V when connecting to TTL family

-Figures show voltage ranges

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C C B A B A

Y = ( + ).( + + ).

Example 4.8: Write the output expression and truth table of the below circuit.

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Y4=?

Example 4.9:

Write the output expression and truth table of the below circuit.

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Example 4.11: There is the following expression:

a Draw the circuit of the above expression.

b Write its truth table.

) (

)

CA

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-Take a look Examples from pages

- Answer Review questions at papge

- Homework

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The End

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