Post on 03-Apr-2018
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MCT-212: DIGITAL LOGIC
DESIGN
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DIGITAL LOGICDESIGNLets start by being literal
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What does each of these words mean?
DIGITAL LOGIC DESIGN
Three words: Digital
Logic
Design
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ANALOG AND DIGITAL QUANTITIES
Analog quantities have
continuous values Digital quantities have a
discrete set of values
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ANALOG AND DIGITAL QUANTITIES
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ANALOG AND DIGITAL QUANTITIES
Types of electronic devices or instruments: Analog
Digital
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ANALOG AND DIGITAL QUANTITIES
Combination of analog and digital:
Give 5 examples of digital and analog
devices each from around you.
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DESIGN
A Design is a creative plan or convention for theconstruction of an object or a system.
What is the engineering design process?
Why is design important?One PROBLEM IDENTIFICTION
Two GENERATING POSSIBLE SOLUTIONS
Three SELECTING A SOLUTION
Four CREATING A PROTOTYPE
Five REFINING THE DESIGN
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LOGIC AND BOOLEAN ALGEBRA
What is Logic?
What Boolean Algebra?
What is Logic Design?
What is Digital Design?
What is Circuit Design or
Digital Logic Design?
LOGICBOOLEAN
ALGEBRA
LOGIC
DESIGN
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LOGIC AND BOOLEAN ALGEBRA
English mathematician, Philosopher
and Logician, Goerge Boole (1815-
1864).
Boolean Algebra, developed in 1854by George Boole in his book An
Investigation of the Laws of Thought.
Computer hardware works with
binary numbers, but binaryarithmetic is much more old than the
computers. [Ancient Chinese
(3000B.C), Ancient Greek (2000B.C),
Boolean Algebra (1850)]
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PROPOSITIONAL LOGIC
The ancient Greek philosophers created a system to
formulize arguments, called propositional logic.
A proposition is a statement that could be TRUE or
FALSE.
Propositions could be compounded by means of the
operators AND, OR and NOT.
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PROPOSITIONAL CALCULUS EXAMPLE
We can assign values to propositions, for example:
I will take an umbrella if and only if it is raining OR the
weather forecast is bad
The proposition I will take an umbrella is the result ofthe Boolean combination (OR) between raining and
weather forecast being bad.
I will take an umbrella = it is
raining OR the weather forecast isbad
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DIAGRAMMATIC REPRESENTATION
We can think of the umbrella proposition as a
result that we calculate from the weather forecast
and the fact that it is raining by means of a
logical OR.
OR
Rain
Bad Weather
Forecast
Take Umbrella
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DIAGRAMMATIC REPRESENTATION
Since propositions can only take two values, we
can express all possible outcomes of the
umbrella proposition by a table:
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MORE COMPLEX PROPOSITIONS
We can make our propositions more complex, forexample:
(Take Umbrella ) = ( NOT (Take Car ) ) AND ( (Bad
Forecast) OR (Raining ) )
and as before represent this diagrammatically.
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MORE COMPLEX PROPOSITIONS
ORRaining
Bad Forecast
Take
UmbrellaNOTCarAND
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BOOLEAN ALGEBRA
To perform calculations quickly and efficiently we can usean equivalent, but more succinct notation.
We also need a to have a well-defined semantics for all
the operators, or connectives that we intend to use.
The system we will employ iscalled Boolean Algebra and
satisfies the criteria above.
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FUNDAMENTALS OF BOOLEAN
ALGEBRA
The truth values are replaced by 1 and0:
1 = TRUE
0 = FALSE
Propositions are replaced by variables:
R = it is raining
W = The weather forecast is bad
Operators are replaced by symbols
or' = NOT
or+ = OR or = AND
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FUNDAMENTALS OF BOOLEAN
ALGEBRA
Our previous complex proposition: (Take Umbrella ) = ( NOT (Take Car) ) AND( (Bad Forecast)
OR (Raining ) )
Is formalized by the simpler equation:
U = (C')(W+R)
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LOGIC = BOOLEAN ALGEBRA
Boolean algebra (or Boolean logic) is a logicalcalculus of truth values.
It resembles the algebra of real numbers as
taught in high school, but with the numericoperations of
multiplication xy conjunction xy,
addition x + y disjunction xy negation x complement x
More on Boolean Algebra later on during the semester.
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NUMBER SYSTEMSAND CONVERSIONS
Back to elementary.!
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DECIMAL NUMBER SYSTEM
Any decimal number such as 2610can be representedas:
Two Thousands Plus Six Hundreds Plus One Tens Plus
Zero Units
Or,
2 x + 6 x + 1 x + 0 x
However the convention is to only write the coefficients
and from their position, the power of10 is deduced.
43210. 12
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DECIMAL AND BINARY NUMBER BASES
How many digits does the conventionalnumber system use? What are they?
TEN: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9The decimal number system is knownas base 10 or radix 10.
How many digits does the Binarynumber system use? What are they?
TWO : 1 and 0
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BINARY NUMBER SYSTEM
The binary number system uses only two digits: 1 and 0 Its a base 2 orradix 2 system.
What does this number stand for indecimal system : 101101.01
1x+ 0x+ 1x+ 1x+ 0x+
1x
. 0x
+ 1x
= 45.25
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OCTAL AND HEXADECIMAL SYSTEMS
Octal number system is the base 8 system, whilehexadecimal system is the base 16 system.
How many, and what digits do Octal and
Hexadecimal systems have?
OCTAL(8) : 0,1,2,3,4,5,6,7
HEXADECIMAL(16) : 0, 1, 2, 3, 4, 5, 6,
7, 8, 9, A, B, C, D, E, F
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ARITHMETIC OPERATIONS
Arithmetic operations like multiplication, division,addition and subtraction can be done the same way
like for the decimal (base10) system.
One must take care not to use any digit other than the
ones allowed for that particular base.
Perform the following operations
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NUMBER BASE CONVERSIONS
How to write:
(100)10
(100)8
(100)2
Decimal
Hexade-cimal
Binary
Octal
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COMPLEMENT OF ANUMBER
The what?!
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COMPLEMENT OF A NUMBER
Complements are used in digital numbers to simplify themultiplication and subtraction process.
There are two types of complements for each base-r system:
(r-1)scomplement
rscomplement
For a numberN:
(r-1)scomplement = ()
rs complement =
for N>0; 0 for N=0= (())+
Complement of the complement of a number, is the
number itself!
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ANY QUESTIONS?
Anyone willing to present?
Time allowed : 5 mins
Topic : Any Bonus Points : +3
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REFERENCES
Chapter no 1: Binary Systems Digi tal Lo gic Designby Morris Mano
Chapter no 1: Digital Concepts
Digi tal Fundamentalsby Floyd