ee089-digital technique 2-th-inst.pdf

7/25/2019 EE089-Digital Technique 2-Th-Inst.pdf

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SRI LANKA INSTITUTE of ADVANCED TECHNOLOGICAL EDUCATION

Training Unit

Digital Technique 2Theory

No: EE 089

INDUSTRIETECHNIKINDUSTRIETECHNIK

ELECTRICAL and ELECTRONIC

ENGINEERING

Instructor Manual


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Training Unit

Digital Technique 2

Theoretical Part

No.: EE 089

Edition: 2008All Rights Reserved

Editor: MCE Industrietechnik Linz GmbH & CoEducation and Training Systems, DM-1Lunzerstrasse 64 P.O.Box 36, A 4031 Linz / AustriaTel. (+ 43 / 732) 6987 3475Fax (+ 43 / 732) 6980 4271Website: www.mcelinz.com


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DIGITAL TECHNIQUE 2

CONTENTS Page

LEARNING OBJECTIVES...................................................................................................4

1 BINARY VARIABLES ...................................................................................................5

1.1

Truth Table...........................................................................................................6

1.2

Logic Types..........................................................................................................7

1.2.1 Positive logic ....................................................................................................7

1.2.2 Negative logic...................................................................................................7

1.2.3

Neutral logic .....................................................................................................8

2 LOGICAL BASIC CIRCUITS ........................................................................................9

2.1

AND function........................................................................................................9

2.1.1 (Conjunction) AND gate ...................................................................................9

2.1.2

Contact-associated AND logic operation: ........................................................9

2.1.3 Basic wiring diagram of an AND function with diodes....................................11

2.1.4

Other symbols instead of (AND) .................................................................12

2.2 OR-Function.......................................................................................................13

2.2.1 (Disjunction) OR gate.....................................................................................13

2.2.2

Contact-associated OR connection................................................................13

2.2.3 Basic Wring diagram of an AND function with diodes....................................14

2.2.4

Another symbol instead of V (or):...................................................................15

2.3 NOT-function......................................................................................................16

2.3.1

(Negation, inversion, conversion) NOT gate.................................................. 16

2.3.2 Contact-associated NOT-function..................................................................16

2.3.3 NOT-circuit with transistor..............................................................................17

2.4 NAND function ...................................................................................................18

2.5

AND-NAND Function .........................................................................................20

2.6

NOR Function ....................................................................................................21

2.7 OR-NOR function...............................................................................................22


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3 LOGIC FUNCTIONS ..................................................................................................26

3.1

The inhibition......................................................................................................26

3.2 Function tables...................................................................................................27

3.3 The implication (inclusion) ................................................................................. 27

3.4 The anti-valence (XOR circuit)...........................................................................28

3.5 Configuration of a XOR circuit with AND gate ................................................... 29

3.6 The equivalency (NOXOR) ................................................................................30

3.7

Configuration of a NOXOR circuit with AND gate ..............................................32

3.8

The trivial logic functions....................................................................................33

4 SUMMARIZATION OF THE LOGICAL BASIC CIRCUITS.........................................34

5

EXERCISES...............................................................................................................35


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DIGITAL TECHNIQUE 2

LEARNING OBJECTIVES

The trainee should...

explain Input and output variables

prepare and evaluate truth tables

allocate voltage potentials to their respective types of logic

explain the logical basic circuits as contact circuits and diode gates prepare truth

tables of the logical basic circuits

explain NOR and NAND gates with transistors

explain other logic functions, such as implications, inhibitions, equivalency and anti-

valency

give the trivial logic functions

allocate the outputs of two Input variables to their logic functions


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DIGITAL TECHNIQUE 2

1 BINARY VARIABLES

Conventional contact controls are a configuration of combinations of normally open

contacts and normally closed contacts. All switch combinations are based on series and

parallel circuits.

The contacts are independent Input variables.

The controlled electric element (e.g., a contactor) represents the dependent output

variable.

Examples:Contact A closed, contact B open: Contactor Q does not pull in.

Contacts A and B closed:

Contactor Q pulls in.

A, B, and 0 are called BOOLEAN VARIABLES.

Note:

George Boole, an Englishman, developed a system for the formal treatment of bivalent

statements.

Each of these variables can exist only in two states:

Contact closed contact not closed

Contactor has pulled in contactor has not pulled in

Closed open

Accomplished not accomplished.

These states are always mutually exclusive.

NOTE:

Two mutually exclusive states are called BINARY STATES.


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These statements are allocated the symbols 1 and 0.

1 means: closed or accomplished (YES)

0 means: open, not accomplished (NO)

Often the symbols L and 0 are used instead of 1 and 0, to be distinguished from the

decimal system. Lately, the allocation H (= high) and L (= low) has been in use, especially

for data sheets; thus, H = 1, L = 0.

The technical realisation of binary states is very simple. Every switch, for example, has

only two states: ON - OFF.

1.1 Truth Table

For Illustration of the functional relationship between the independent Input variables A

and B, and the dependent output variables Q, the so-called truth or function tables are

used.

Example for a simple truth table:


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1.2 Logic Types

In electronic digital technology, usually electric potentials are being allocated to the binary

states 1 and 0. Depending on the allocation, we talk of positive logic, negative logic, or

neutral logic.

For a positive logic, the 1 -signal is more positive than the 0-signal.

In negative logic, the 1 -signal is more negative than the 0-signal.

1.2.1 Positive logic

1.2.2 Negative logic


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1.2.3 Neutral logic

As the figure shows, the 1- or 0-signal corresponds to a defined voltage value with a

certain range of tolerance.

It has been mentioned before that nowadays in many papers, descriptions , and data

sheets the terms Low (L) and High (H) are used today instead of 0 and 1 (0 and L). This is

the so-called neutral logic and it is used to express that the H signal is more positive than

the L-signal, with the potentials also sometimes being negative.

These terms come from US language usage; they avoid the difficulties in expressing

positive and negative logics. In case of circuit-related technical problems, L and H provide

reasonable explanations of theoretical principles,

For realisations, 1 and 0 seem can be more easily understood, especially truth tables

displaying 1 and 0 are much more clear.


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2 LOGICAL BASIC CIRCUITS

All logic decisions of binary data processing can be realised with the three basic functions

AND, OR, and NOT.

2.1 AND function

2.1.1 (Conjunction) AND gate

Symbol: Old: New:

The AND function has at least two Input variables (A, B, ...).

The output Q has the "1" signal if all inputs have the "1" signal.

Example: The elevator starts as soon as the door is closed and after the floor

pushbutton has been actuated.

2.1.2 Contact-associated AND logic operation:


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Description:

Only after the switches A and B and C have been closed, the output Q (contactor coil) will

be energized.


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Truth table:

2.1.3 Basic wiring diagram of an AND function with diodes

Circuit possibilities:

Function:

Q = A B C

That is:

Q is equal to A and B and C

Symbol:


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Description:

If the Inputs A and B are in contact with 0V then both diodes are in conduction direction.

The entire voltage drops at the resistance. The output Q is also in contact with 0V ("0"-

signal).

If an Input (A or B) is set to a "1" signal, always one diode remains conducting. Only after

both Inputs have the "1" signal no current flows any more via the diodes, so that there is

no voltage drop at the resistance. The output Q carries the "1" signal.

Truth Table:

2.1.4 Other symbols instead of (AND)

Q = A . B Q = A B

NOTE:

The AND connection has the "1" signal at the output Q only if all inputs A, B, C, also

have the "1" signal.

Function:

Q = A B

Symbol:

Old: New


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2.2 OR-Function

2.2.1 (Disjunction) OR gate

Symbol: Old: New:

The OR function has at least two input variables (A, B, C. ...)

The output Q carries the "1" signal if at least one input carries the "1" Signal.

Example:

The motor must be switched off if the winding gets too warm or if the power is too high.

2.2.2 Contact-associated OR connection

Description:

Even if only one of the inputs A or B or C is closed, there is voltage at the output Q

(contactor coil).


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Truth table: Function:

Q = A v B v C

This means:

Q equals A or B or C

Symbol:

Old: New:

2.2.3 Basic Wring diagram of an AND function with diodes

Circuit possibilities:


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Description:

If both inputs are in contact with OV, no current will flow (no voltage drop at the resistor

R). The output Q has the "0" signal.

If a "1" signal is applied to one of the two inputs then one of the two diodes becomes

conducting. The entire voltage drops at the resistor R.

The output Q has the "1" signal.


Q = A v B

Old: New:

2.2.4 Another symbol instead of V (or):

A = A + B

NOTE:

The OR connection has the "1" signal at the output Q if at least one Input has the "1"

signal.


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2.3 NOT-function

2.3.1 (Negation, inversion, conversion) NOT gate

Symbols: Old: New:

Switching effects a Signal conversion.

Example:

A folding machine can be switched an only if the hands of the operator are NOT within the

hazardous area.

2.3.2 Contact-associated NOT-function

Description:

The alarm siren does not sound if the relay is under voltage.



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2.3.3 NOT-circuit with transistor

Wiring possibilities:

Description:

If Input A has a "0" signal, the transistor is locked, Q has a "1" signal.

If Input A has a "1" signal, the transistor is conducting, Q has a "0" signal.


NOTE:

The transistor activates a Signal conversion.


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2.4 NAND function

Symbol: Old: New:

The NAND function is a combination of an AND function which is followed by a NOT

function.

Circuit:


Description:

If there is a 0" signal on both inputs (transistors are locked) then output Q has a "1"

signal:


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If a "1" signal is applied to one of the inputs, still one of the transistors will remain locked.

Output Q has a "1" signal.

Only if both inputs have the "1" signal then current will flow (IC) and the output Q will have

the 0 Signal.


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2.5 AND-NAND Function

Symbol Old: New:

Circuit:



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2.6 NOR Function

Symbol Old: New:

The NOR function is an OR function which is followed by a NOT function.

Circuit:


Description:

If the inputs A and B have a "0" signal, then both transistors are locked, Output Q has the

"1" signal. If a "1" signal is applied to the basis of a transistor, then the transistor performs

a fully advanced control, current flows (IC) and the entire voltage drops at the resistor

(RC). The output Q has a "0" signal.


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2.7 OR-NOR function

Symbol: Old: New

Circuit:



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Exercises:

On the basis of the texts, prepare a logic circuit with the associated formula:

1. If you want to smoke, several criteria will have to be fulfilled until the cigarette of the

pipe is burning:

a) Cigarette AND fire AND the desire to smoke,

OR

b) b) Pipe AND tobacco AND fire AND the desire to smoke.

Furthermore, it must be assured that

c) you do NOT sleep OR sleep at that moment

Solve the exercise with "AND", "OR" and "NOT".

Logic diagram:

Function:


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2. Lowering the beam of a folding press

A = main motor

B = pre-selector switch for inching operation

C = pedal

D = light barrier (photoelectric barrier)

E = pre-selector for single strake

F = pre-selector for continuous strake

G = switch for two-hand safety device

H = pushbutton for two-hand safety device

K = pushbutton for two-hand safety device.


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The beam of a folding press can be lowered only if:

- the main motor A is switched on

- the pre-selector switch has been set to inching operation

- the pedal is actuated AND the light barrier D is NOT interrupted

- OR if

- the main motor A is switched on

- the pre-selector is switched to single stroke E OR continuous stroke F,

- the two-hand safety device G is switched on AND the pushbuttons H and K have been

pressed by the operator

- the pedal C has been actuated AND, furthermore, the light barrier D is NOT

interrupted

Solve this exercise with "AND", "OR" and "NOT".

Logic diagram:

Function:


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3 LOGIC FUNCTIONS

3.1 The inhibition

The inhibition is a special form of the conjunction (AND form). One of the two Input

quantities is first negated.

Is inhibition A

Is inhibition B

Inhibition A:

Inhibition B:

Inhibition A: Symbol:

Inhibition B: Symbol:


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3.2 Function tables

3.3 The implication (inclusion)

The implication is a special form of disjunction (OR-function). One of the two Input

quantities is first negated.

Is implication A

Is implication B

Implication A:

Implication B:

Implication A: Symbol:


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Implication B: Symbol:

3.4 The anti-valence (XOR circuit)

Symbol: Old: New:

The output of the anti-valence circuit has the "1" signal if the two Inputs don't have the

same signals.


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Truth table:

Except for the last line the result is equal to an OR function. This means that the last

combination is excluded.

Its name, therefore: "EXCLUSIVE-OR= XOR.

3.5 Configuration of a XOR circuit with AND gate


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Truth table:

Function:

3.6 The equivalency (NOXOR)

Symbol: Old: New

The output of the equivalency circuit has the "1" signal if both inputs have the same

signal.


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Truth table:

The switching operation is a negation of the XOR function. Consequently, its name:

"NOXOR" from NOT EXCLUSIVE OR.


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3.7 Configuration of a NOXOR circuit with AND gate

Truth table:

Function:


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3.8 The trivial logic functions

(Trivial = insignificant, not important)

They do not lead to a logical answer.

1. constant "0000"

2. constant 1 "1111"

3. Identity A "0011"

4. Identity B "0101"


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4 SUMMARIZATION OF THE LOGICAL BASIC CIRCUITS


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5 EXERCISES

a) The signal-time-diagram of two Input variables has the following picture.

Draw the associated outputs for:

Q1 = AND, Q2 = NOR, Q3 = anti-valency, Q4 = OR

Q5 = inhibition A, Q6 = implication, Q7 = HAND


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b) Draw the Logic circuit for the following contact circuits, prepare the truth table and the

function


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c) Write the function from this logic circuit and draw the contact circuit.

d) Draw the logic and contact circuits and prepare the truth table for this function:

Truth table:


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EE089 - Digital Technique 2

Theoretical Test


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DIGITAL TECHNIQUE 2

TEST 1

1. Draw an AND circuit with diodes for three Input variables and prepare the related

Truth table.

2. Draw a transistorized circuit for this Truth table.

3. The signal-time diagram of two Input variables has the following picture.

Draw the output signal for a XOR.

4. Draw the logic circuit of an implication A.

Prepare the related truth table and the function.


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5. Complete the logic circuit of the NOXOR circuit.

6. Draw and name the logic symbols of the two outputs of this signal-time diagram.

7. Which logic function has the "1" signal at the output Q if the Input variable A is smaller

than the variable B?

8. Name two gate types with which all logic circuit problems can be solved.


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9. Which logic function has the "1" signal at the output Q if at least one Input variable has

the "0" signal?

10. Draw the logic circuit diagram for this function:

11. Draw an OR circuit with diodes for three Input variables and prepare the associated

truth table.

12. Draw a transistor circuit for the following truth table.

13. The signal-time diagram of two Input variables has the following picture.

Draw the output signal for a NOXOR.

14. Draw the logic circuit of an inhibition B. Prepare the associated truth table and the

function.


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15. Complete the logic circuit of the XOR circuit.

16. Draw and name the logic symbols of both outputs of this signal-time

17. Which logic function has a "0" signal at the output Q if the Input variable A is smaller

than the variable B?


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18. Which logic function has the "0" signal at the output Q if at least one Input variable has

the "1" signal?

19. Draw the logic circuit for this function:

20. Write the function from this circuit:


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DIGITAL TECHNIQUE 2

TEST 1

(Solution)

1.

2.

3.


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4.

5.

6.

7.


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8. NOR function, NAND function

9. NAND -function

10.

11.


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12.

13.

14.


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15.

16.

17. Implication B

18. NOR function


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19.

20.


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KEY TO EVALUATION

PER CENT MARK

88 100 1

75 87 2

62 74 3

50 61 4

0 49 5

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