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Basic Digital Logic(Lab Session)
Ferdinand M Fernando
Asst. Professor I
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Basic Digital Logic
Review
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Review
Digital Electronics makes use of 2states:
Logic High, or 1
Logic Low, or 0
Logic Circuit F. M. Fernando URSM-College of Engineering
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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.
Logic Circuit F. M. Fernando URSM-College of Engineering
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Review Questions
What is the outcome of the following:
1
1
0
1
0
1
1
Logic Circuit F. M. Fernando URSM-College of Engineering
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0 0
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Standard Logic Symbols Basedon ANSI/IEEE Std. 91-1984
Logic Circuit F. M. Fernando URSM-College of Engineering
The Inverter
The inverter (NOT circuit) performsthe operation called inversionorcomplementation.
Standard logic symbols:
1
1
input output input output
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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
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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
Logic Circuit F. M. Fernando URSM-College of Engineering 11
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
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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
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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.
Logic Circuit F. M. Fernando URSM-College of Engineering
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
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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?
Logic Circuit F. M. Fernando URSM-College of Engineering
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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.
Logic Circuit F. M. Fernando URSM-College of Engineering
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
Logic Circuit F. M. Fernando URSM-College of Engineering27
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.
Logic Circuit F. M. Fernando URSM-College of Engineering29
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
Logic Circuit F. M. Fernando URSM-College of Engineering31
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)
Logic Circuit F. M. Fernando URSM-College of Engineering
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)
Logic Circuit F. M. Fernando URSM-College of Engineering
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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
3838Logic 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
Logic Circuit F. M. Fernando URSM-College of Engineering
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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
414141Logic Circuit F. M. Fernando URSM-College of Engineering
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NUMBERING SYSTEM FORDIGITAL ICs
424242Logic Circuit F. M. Fernando URSM-College of Engineering
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4343
NUMBERING SYSTEM FORDIGITAL ICs
434343Logic Circuit F. M. Fernando URSM-College of Engineering
4444444444Logic Circuit F. M. Fernando URSM-College of Engineering
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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.
Logic Circuit F. M. Fernando URSM-College of Engineering