2-Basic Digital Logic - LAB

8/10/2019 2-Basic Digital Logic - LAB

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Basic Digital Logic(Lab Session)

Ferdinand M Fernando

Asst. Professor I

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Basic Digital Logic

Review

Logic Circuit F. M. Fernando URSM-College of Engineering


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Review

Digital Electronics makes use of 2states:

Logic High, or 1

Logic Low, or 0


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Review

There are 3 basic digital gates:

AND

OR

NOT



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Review

AND, where ALL inputs must be 1for the output to be 1

OR, where ANY of the inputs can be 1for the output to be 1

NOT (or the Inverter) where theoutput is the opposite(compliment) of the input.


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Review Questions

What is the outcome of the following:

1

1

0

1

0

1

1


11

0 0


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Standard Logic Symbols Basedon ANSI/IEEE Std. 91-1984


The Inverter

The inverter (NOT circuit) performsthe operation called inversionorcomplementation.

Standard logic symbols:

1

1

input output input output

Logic Circuit F. M. Fernando URSM-College of Engineering 8


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Inverter Truth Table & LogicExpression

Input Output

LOW (0) HIGH (1)

HIGH (1) LOW (0)

A X = A

0 1

1 0


The AND Gate & ItsOperation

The AND gate is composed of two ormore inputs and a single output.

For a 2-input AND gate: Output X is HIGH only when inputs A

and B are HIGH

X is LOW when either A or B is LOW, orwhen both A and B are LOW.

&A

BX

A

BX



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AND Gate Truth Table

The total number of possible combinations ofbinary inputs to a gate is determined by:

N = 2n

Therefore: 2 bits (n=2) = 4 combinations 3 bits = 8 combinations 4 bits = 16 combinations

INPUTS OUTPUT

A B X

0 0 0

0 1 0

1 0 0

1 1 1

A

BX


AND Gate LogicExpressions

Use either:

X = A B,or

X = AB

If there are more than 2 inputs, do as

below:

A

BX

X= ABC

X= ABCD

ABC

ABCD



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The OR Gate

Like AND gate, an OR gate has twoor more inputs and one output.

For a 2-input OR gate: output X is HIGH when either input A or

input B is HIGH, or when both A and Bare HIGH.

X is LOW only when both A and B areLOW.

A

BX

1A

B

X


OR Gate Truth Table

INPUTS OUTPUT

A B X

0 0 0

0 1 1

1 0 1

1 1 1

A

BX



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OR Gate Logic Expressions

Use the operator + for OR operation

X = A + B

If there are more than 2 inputs, do asbelow:

X= A+B+C

X= A+B+C+D

ABC

ABCD


Basic Digital Logic

Basic Combinational Logic,NAND and NOR gates

(Lab Session)



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Combinational Logic

A circuit that utilizes more that 1logic function has CombinationalLogic.

As an example, if a circuit has anAND gate connected to an Inverter

gate, this circuit has combinationallogic.


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Combinational logic

How would your describe the outputof this combinational logic circuit?



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NAND Gate

The NAND gate is the combinationof an NOT gate with an AND gate.

The Bubble in front of the gate is an inverter.


The NAND Gate

NAND = NOT-AND

For a 2-input NAND gate:

Output X is LOW only when inputs Aand B are HIGH

X is HIGH when either A or B is LOW, orwhen both A and B are LOW

&A

BX

A

BX

A

BX



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NAND Gate Truth Table & LogicExpression

INPUTS OUTPUT

A B X

0 0 1

0 1 1

1 0 1

1 1 0

A

B X

The Boolean expression for theoutput of a 2-input NAND gate is

X = AB

Logic Circuit F. M. Fernando URSM-College of Engineering21

Negative-OR Equivalent of aNAND

For a 2-input NAND gate performinga negative-OR operation

Output X is HIGH when either input A orinput B is LOW or when both A and B

are LOW

NAND Negative-OR



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Combinational logic

How would your describe the outputof this combinational logic circuit?


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NOR gate

The NOR gate is the combination ofthe NOT gate with the OR gate.

The Bubble in front of the gate is an inverter.



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NAND and NOR gates

The NAND and NOR gates are verypopular as they can be connected inmore ways that the simple AND andOR gates.


The NOR Gate

NOR = NOT-OR

For a 2-input NOR gate: Output X is LOW when either input A or

input B is HIGH, or when both A and Bare HIGH

X is HIGH only when both A and B areLOW

A

BX

A

BX

1A

BX



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NOR Gate Truth Table & LogicExpression

INPUTS OUTPUT

A B X

0 0 1

0 1 0

1 0 0

1 1 0

The Boolean expression for theoutput of a 2-input NOR gate is

X = A+B

A

B X


Negative-AND Equivalent of aNOR

For a 2-input NOR gate performing anegative-AND operation

Output X is HIGH only when both inputsA and B are LOW

NOR Negative-AND



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The XOR and XNOR Gates

Exclusive-OR and Exclusive-NORgates are formed by a combinationof other gates already discussed.

Because of their fundamentalimportance in many applications,these gates are often treated asbasic logic elements with their ownunique symbols.


The XOR Gate

For a 2-input exclusive-OR gate: Output X is HIGH when input A is LOW

and input B is HIGH, or when input A isHIGH and input B is LOW

X is LOW when A and B are both HIGHand both LOW

= 1A

B

X

A

BX



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XOR Gate Truth Table & LogicExpression

INPUTS OUTPUT

A B X

0 0 0

0 1 1

1 0 1

1 1 0

The Boolean expression for theoutput of a 2-input XOR gate is

X = A+B

A

B X


The XNOR Gate

For a 2-input exclusive-NOR gate: Output X is LOW when input A is LOW

and input B is HIGH, or when input A isHIGH and input B is LOW

X is HIGH when A and B are both HIGHand both LOW

= 1A

B

X

A

B

X



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XNOR Gate Truth Table & LogicExpression

INPUTS OUTPUT

A B X

0 0 1

0 1 0

1 0 0

1 1 1

The Boolean expression for theoutput of a 2-input XNOR gate is

X = A+B

A

B X


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Exercise (a bit challenging)


Turn the NAND and NOR gates into

inverter (NOT) gates. Include a

switch for the input.


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Basic Digital Logic

Chips and Gates

(Lab Session)


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Basic Digital Chips

Digital Electronics devices areusually in a chip format.

The chip is identified with a partnumber or a model number.

A standard series starts withnumbers 74, 4, or 14. 7404 is an inverter

7408 is an AND

7432 is an OR

7400 is a NAND



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7400 Series TTLIntegrated Circuit

7400 - NAND (four gates per chip)

7402 - NOR (four gates per chip)

7404 - NOT (six gates per chip)

7408 - AND (four gates per chip)

7432 - OR (four gates per chip)

7486 - XOR (four gates per chip)

3737Logic Circuit F. M. Fernando URSM-College of Engineering



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Chips Pinouts

Basic logic chipsoften come in 14-pinpackages.

Package sizes andstyles vary.

Pin 1 is indicatedwith a dot or half-circle

Numbers are readcounter-clockwisefrom pin 1 (viewedfrom the top)

Pin 1 Pin 7

Pin 14 Pin 8


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Chips Pinouts

Chips require avoltage to function

Vcc is equal to 5

volts and is typicallypin 14

Ground is typicallypin 7

Pin 1 Pin 7

Pin 14 Pin 8



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NUMBERING SYSTEM FORDIGITAL ICs


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4343





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Wiring a chip

Vcc

Vcc

IN

IN

OUT

LED orProbe


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Layout of the (Logic TrainerKit) Experimenter's Board



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Flat Side

Wires

7400

Component Placement onBreadboard


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Equivalent Logic Diagram



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Case Project 1(Guessing Game)

Using the 74XX series IC, build an equivalent of the logic

game that works as follows:

a) One player, using 4 switches, creates a 4-bit combination.

These switches are hidden from his opponent.

b) Another player will try to guess the combination of the 4

switches using another set of switches.

c) A BLUE LED will indicate whether the combination of the 4

hidden switches is correct. If any of the switches is incorrect, a

RED LED will be ON instead. The LEDs cannot be both ON.

Solution should include at least 3 proposed circuit designs andyour recommendation which among these circuits is your choice

with corresponding justification.


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2-Basic Digital Logic - LAB