The document discusses digital electronics and Boolean algebra. It introduces basic logic operations such as AND, OR, and NOT. It then discusses additional logic operations like NAND, NOR, XOR, and XNOR. Truth tables are presented as a way to describe the functional behavior of Boolean expressions and logic circuits. Boolean expressions are composed of literals and logic operations. Boolean algebra laws and theorems can be used to simplify Boolean expressions, which allows for simpler circuit implementation.
flip flop,introduction,types,. SR Flip Flop
a.SR Flip Flop Active Low = NAND gate Latch
b. SR Flip Flop Active High = NOR gate Latch
2. Clocked SR Flip Flop
3. JK Flip Flop
4. JK Flip Flop With Pre-set And Clear
5. T Flip Flop
6. D Flip Flop
7. Master-Slave Edge-Triggered Flip-Flop
The Used of Flip Flop:
Computers and calculators use
Flip-flop for their memory??
A flip flop is an electronic circuit with two stable states(High/Low) that can be used to store binary data.
This topic introduces the numbering systems: decimal, binary, octal and hexadecimal. The topic covers the conversion between numbering systems, binary arithmetic, one's complement, two's complement, signed number and coding system. This topic also covers the digital logic components.
flip flop,introduction,types,. SR Flip Flop
a.SR Flip Flop Active Low = NAND gate Latch
b. SR Flip Flop Active High = NOR gate Latch
2. Clocked SR Flip Flop
3. JK Flip Flop
4. JK Flip Flop With Pre-set And Clear
5. T Flip Flop
6. D Flip Flop
7. Master-Slave Edge-Triggered Flip-Flop
The Used of Flip Flop:
Computers and calculators use
Flip-flop for their memory??
A flip flop is an electronic circuit with two stable states(High/Low) that can be used to store binary data.
This topic introduces the numbering systems: decimal, binary, octal and hexadecimal. The topic covers the conversion between numbering systems, binary arithmetic, one's complement, two's complement, signed number and coding system. This topic also covers the digital logic components.
Definition of finite state automaton: computation. It is an abstract machine that can be in exactly one of a finite number of states at any given time. The FSM can change from one state to another in response to some external inputs; the change from one state to another is called a transition. A FSM is defined by a list of its states, its initial state, and the conditions for each transition.
the report contain
Introduction
The historical of finite state automaton
Types of FSA
The advantages and disadvantages of FSA
examples for FSA
عمار عبد الكريم صاحب مبارك
AmmAr Abdualkareem sahib mobark
In electronics, an adder is a digital circuit that performs addition of numbers.
In modern computers and other kinds of processors, adders are used in the arithmetic logic unit (ALU), but also in other parts of the processor, where they are used to calculate addresses, table indices, and similar operations.
GIVES A DETAILED PRESENTATION OF SYNCHRONOUS SEQUENTIAL
CIRCUITS (FINITE STATE MACHINES). IT EXPLAINS THE BEHAVIOR OF THESE
CIRCUITS AND DEVELOPS PRACTICAL DESIGN TECHNIQUES FOR BOTH
MANUAL AND AUTOMATED DESIGN. DEALS WITH A GENERAL CLASS OF
CIRCUITS IN WHICH THE OUTPUTS DEPEND ON THE PAST BEHAVIOR OF THE
CIRCUIT, AS WELL AS ON THE PRESENT VALUES OF INPUTS. THEY ARE
CALLED SEQUENTIAL CIRCUITS. IN MOST CASES A CLOCK SIGNAL IS USED TO
CONTROL THE OPERATION OF A SEQUENTIAL CIRCUIT; SUCH A CIRCUIT IS
CALLED A SYNCHRONOUS SEQUENTIAL CIRCUIT.
Definition of finite state automaton: computation. It is an abstract machine that can be in exactly one of a finite number of states at any given time. The FSM can change from one state to another in response to some external inputs; the change from one state to another is called a transition. A FSM is defined by a list of its states, its initial state, and the conditions for each transition.
the report contain
Introduction
The historical of finite state automaton
Types of FSA
The advantages and disadvantages of FSA
examples for FSA
عمار عبد الكريم صاحب مبارك
AmmAr Abdualkareem sahib mobark
In electronics, an adder is a digital circuit that performs addition of numbers.
In modern computers and other kinds of processors, adders are used in the arithmetic logic unit (ALU), but also in other parts of the processor, where they are used to calculate addresses, table indices, and similar operations.
GIVES A DETAILED PRESENTATION OF SYNCHRONOUS SEQUENTIAL
CIRCUITS (FINITE STATE MACHINES). IT EXPLAINS THE BEHAVIOR OF THESE
CIRCUITS AND DEVELOPS PRACTICAL DESIGN TECHNIQUES FOR BOTH
MANUAL AND AUTOMATED DESIGN. DEALS WITH A GENERAL CLASS OF
CIRCUITS IN WHICH THE OUTPUTS DEPEND ON THE PAST BEHAVIOR OF THE
CIRCUIT, AS WELL AS ON THE PRESENT VALUES OF INPUTS. THEY ARE
CALLED SEQUENTIAL CIRCUITS. IN MOST CASES A CLOCK SIGNAL IS USED TO
CONTROL THE OPERATION OF A SEQUENTIAL CIRCUIT; SUCH A CIRCUIT IS
CALLED A SYNCHRONOUS SEQUENTIAL CIRCUIT.
To Download this click on the link below:-
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Number System
Decimal Number System
Binary Number System
Why Binary?
Octal Number System
Hexadecimal Number System
Relationship between Hexadecimal, Octal, Decimal, and Binary
Number Conversions
June 3, 2024 Anti-Semitism Letter Sent to MIT President Kornbluth and MIT Cor...Levi Shapiro
Letter from the Congress of the United States regarding Anti-Semitism sent June 3rd to MIT President Sally Kornbluth, MIT Corp Chair, Mark Gorenberg
Dear Dr. Kornbluth and Mr. Gorenberg,
The US House of Representatives is deeply concerned by ongoing and pervasive acts of antisemitic
harassment and intimidation at the Massachusetts Institute of Technology (MIT). Failing to act decisively to ensure a safe learning environment for all students would be a grave dereliction of your responsibilities as President of MIT and Chair of the MIT Corporation.
This Congress will not stand idly by and allow an environment hostile to Jewish students to persist. The House believes that your institution is in violation of Title VI of the Civil Rights Act, and the inability or
unwillingness to rectify this violation through action requires accountability.
Postsecondary education is a unique opportunity for students to learn and have their ideas and beliefs challenged. However, universities receiving hundreds of millions of federal funds annually have denied
students that opportunity and have been hijacked to become venues for the promotion of terrorism, antisemitic harassment and intimidation, unlawful encampments, and in some cases, assaults and riots.
The House of Representatives will not countenance the use of federal funds to indoctrinate students into hateful, antisemitic, anti-American supporters of terrorism. Investigations into campus antisemitism by the Committee on Education and the Workforce and the Committee on Ways and Means have been expanded into a Congress-wide probe across all relevant jurisdictions to address this national crisis. The undersigned Committees will conduct oversight into the use of federal funds at MIT and its learning environment under authorities granted to each Committee.
• The Committee on Education and the Workforce has been investigating your institution since December 7, 2023. The Committee has broad jurisdiction over postsecondary education, including its compliance with Title VI of the Civil Rights Act, campus safety concerns over disruptions to the learning environment, and the awarding of federal student aid under the Higher Education Act.
• The Committee on Oversight and Accountability is investigating the sources of funding and other support flowing to groups espousing pro-Hamas propaganda and engaged in antisemitic harassment and intimidation of students. The Committee on Oversight and Accountability is the principal oversight committee of the US House of Representatives and has broad authority to investigate “any matter” at “any time” under House Rule X.
• The Committee on Ways and Means has been investigating several universities since November 15, 2023, when the Committee held a hearing entitled From Ivory Towers to Dark Corners: Investigating the Nexus Between Antisemitism, Tax-Exempt Universities, and Terror Financing. The Committee followed the hearing with letters to those institutions on January 10, 202
Unit 8 - Information and Communication Technology (Paper I).pdfThiyagu K
This slides describes the basic concepts of ICT, basics of Email, Emerging Technology and Digital Initiatives in Education. This presentations aligns with the UGC Paper I syllabus.
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http://sandymillin.wordpress.com/iateflwebinar2024
Published classroom materials form the basis of syllabuses, drive teacher professional development, and have a potentially huge influence on learners, teachers and education systems. All teachers also create their own materials, whether a few sentences on a blackboard, a highly-structured fully-realised online course, or anything in between. Despite this, the knowledge and skills needed to create effective language learning materials are rarely part of teacher training, and are mostly learnt by trial and error.
Knowledge and skills frameworks, generally called competency frameworks, for ELT teachers, trainers and managers have existed for a few years now. However, until I created one for my MA dissertation, there wasn’t one drawing together what we need to know and do to be able to effectively produce language learning materials.
This webinar will introduce you to my framework, highlighting the key competencies I identified from my research. It will also show how anybody involved in language teaching (any language, not just English!), teacher training, managing schools or developing language learning materials can benefit from using the framework.
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International FDP on Fundamentals of Research in Social Sciences
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Macroeconomics- Movie Location
This will be used as part of your Personal Professional Portfolio once graded.
Objective:
Prepare a presentation or a paper using research, basic comparative analysis, data organization and application of economic information. You will make an informed assessment of an economic climate outside of the United States to accomplish an entertainment industry objective.
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This slide is special for master students (MIBS & MIFB) in UUM. Also useful for readers who are interested in the topic of contemporary Islamic banking.
6. 6
Additional Logic Operations
NAND
F = (A . B)'
NOR
F = (A + B)'
XOR
Output is 1 iff either input is 1, but not both.
XNOR (aka. Equivalence)
Output is 1 iff both inputs are 1 or both inputs
are 0.
11. 11
Truth Tables
Used to describe the functional behavior of a Boolean
expression and/or Logic circuit.
Each row in the truth table represents a unique
combination of the input variables.
For n input variables, there are 2n rows.
The output of the logic function is defined for each
row.
Each row is assigned a numerical value, with the rows
listed in ascending order.
The order of the input variables defined in the logic
function is important.
15. 13IDP14- Digital Electronics 15
Boolean Expressions
Boolean expressions are composed of
Literals – variables and their complements
Logical operations
Examples
F = A.B'.C + A'.B.C' + A.B.C + A'.B'.C'
F = (A+B+C').(A'+B'+C).(A+B+C)
F = A.B'.C' + A.(B.C' + B'.C)
literals logic operations
16. 13IDP14- Digital Electronics 16
Boolean Expressions
Boolean expressions are realized using a
network (or combination) of logic gates.
Each logic gate implements one of the logic
operations in the Boolean expression
Each input to a logic gate represents one of
the literals in the Boolean expression
f
A
B
logic operationsliterals
17. 13IDP14- Digital Electronics 17
Boolean Expressions
Boolean expressions are evaluated by
Substituting a 0 or 1 for each literal
Calculating the logical value of the expression
A Truth Table specifies the value of the Boolean
expression for every combination of the
variables in the Boolean expression.
For an n-variable Boolean expression, the truth
table has 2n rows (one for each combination).
18. 13IDP14- Digital Electronics 18
Boolean Expressions
Example:
Evaluate the following Boolean expression,
for all combination of inputs, using a Truth
table.
F(A,B,C) = A'.B'.C + A.B'.C' + A.C
19. 13IDP14- Digital Electronics 19
Boolean Expressions
Two Boolean expressions are equivalent if they
have the same value for each combination of
the variables in the Boolean expression.
F1 = (A + B)'
F2 = A'.B'
How do you prove that two Boolean
expressions are equivalent?
Truth table
Boolean Algebra
20. 13IDP14- Digital Electronics 20
Boolean Expressions
Example:
Using a Truth table, prove that the following
two Boolean expressions are equivalent.
F1 = (A + B)'
F2 = A'.B'
22. 13IDP14- Digital Electronics 22
Boolean Algebra
George Boole developed an algebraic description for
processes involving logical thought and reasoning.
Became known as Boolean Algebra
Claude Shannon later demonstrated that Boolean
Algebra could be used to describe switching circuits.
Switching circuits are circuits built from devices that
switch between two states (e.g. 0 and 1).
Switching Algebra is a special case of Boolean
Algebra in which all variables take on just two distinct
values
Boolean Algebra is a powerful tool for analyzing and
designing logic circuits.
23. 13IDP14- Digital Electronics 23
Basic Laws and Theorems
Commutative Law A + B = B + A A.B = B.A
Associative Law A + (B + C) = (A + B) + C A . (B . C) = (A . B) . C
Distributive Law A.(B + C) = AB + AC A + (B . C) = (A + B) . (A + C)
Null Elements A + 1 = 1 A . 0 = 0
Identity A + 0 = A A . 1 = A
A + A = A A . A = A
Complement A + A' = 1 A . A' = 0
Involution A'' = A
Absorption (Covering) A + AB = A A . (A + B) = A
Simplification A + A'B = A + B A . (A' + B) = A . B
DeMorgan's Rule (A + B)' = A'.B' (A . B)' = A' + B'
Logic Adjacency (Combining) AB + AB' = A (A + B) . (A + B') = A
Consensus AB + BC + A'C = AB + A'C (A + B) . (B + C) . (A' + C) = (A + B) . (A' + C)
Idempotence
24. 13IDP14- Digital Electronics 24
Idempotence
A + A = A
F = ABC + ABC' + ABC
F = ABC + ABC'
Note: terms can also be added using this theorem
A . A = A
G = (A' + B + C').(A + B' + C).(A + B' + C)
G = (A' + B + C') + (A + B' + C)
Note: terms can also be added using this theorem
25. 13IDP14- Digital Electronics 25
Complement
A + A' = 1
F = ABC'D + ABCD
F = ABD.(C' + C)
F = ABD
A . A' = 0
G = (A + B + C + D).(A + B' + C + D)
G = (A + C + D) + (B . B')
G = A + C + D
26. 13IDP14- Digital Electronics 26
Distributive Law
A.(B + C) = AB + AC
F = WX.(Y + Z)
F = WXY + WXZ
G = B'.(AC + AD)
G = AB'C + AB'D
H = A.(W'X + WX' + YZ)
H = AW'X + AWX' + AYZ
A + (B.C) = (A + B).(A + C)
F = WX + (Y.Z)
F = (WX + Y).(WX + Z)
G = B' + (A.C.D)
G = (B' + A).(B' + C).(B' + D)
H = A + ( (W'X).(WX') )
H = (A + W'X).(A + WX')
27. 13IDP14- Digital Electronics 27
Absorption (Covering)
A + AB = A
F = A'BC + A'
F = A'
G = XYZ + XY'Z + X'Y'Z' + XZ
G = XYZ + XZ + X'Y'Z'
G = XZ + X'Y'Z'
H = D + DE + DEF
H = D
A.(A + B) = A
F = A'.(A' + BC)
F = A'
G = XZ.(XZ + Y + Y')
G = XZ.(XZ + Y)
G = XZ
H = D.(D + E + EF)
H = D
28. 13IDP14- Digital Electronics 28
Simplification
A + A'B = A + B
F = (XY + Z).(Y'W + Z'V') + (XY + Z)'
F = Y'W + Z'V' + (XY + Z)'
A.(A' + B) = A . B
G = (X + Y).( (X + Y)' + (WZ) )
G = (X + Y) . WZ
29. 13IDP14- Digital Electronics 29
Logic Adjacency (Combining)
A.B + A.B' = A
F = (X + Y).(W'X'Z) + (X + Y).(W'X'Z)'
F = (X + Y)
(A + B).(A + B') = A
G = (XY + X'Z').(XY + (X'Z')' )
G = XY
30. 13IDP14- Digital Electronics 30
Boolean Algebra
Example:
Using Boolean Algebra, simplify the following
Boolean expression.
F(A,B,C) = A'.B.C + A.B'.C + A.B.C
31. 13IDP14- Digital Electronics 31
Boolean Algebra
Example:
Using Boolean Algebra, simplify the following
Boolean expression.
F(A,B,C) = (A'+B'+C').(A'+B+C').(A+B'+C')
32. 13IDP14- Digital Electronics 32
DeMorgan's Laws
Can be stated as follows:
The complement of the product (AND) is the
sum (OR) of the complements.
(X.Y)' = X' + Y'
The complement of the sum (OR) is the
product (AND) of the complements.
(X + Y)' = X' . Y'
Easily generalized to n variables.
Can be proven using a Truth table
35. 13IDP14- Digital Electronics 35
Importance of Boolean Algebra
Boolean Algebra is used to simplify Boolean
expressions.
– Through application of the Laws and Theorems
discussed
Simpler expressions lead to simpler circuit realization,
which, generally, reduces cost, area requirements, and
power consumption.
The objective of the digital circuit designer is to design
and realize optimal digital circuits.
36. 13IDP14- Digital Electronics 36
Algebraic Simplification
Justification for simplifying Boolean expressions:
– Reduces the cost associated with realizing the
expression using logic gates.
– Reduces the area (i.e. silicon) required to fabricate the
switching function.
– Reduces the power consumption of the circuit.
In general, there is no easy way to determine when a
Boolean expression has been simplified to a minimum
number of terms or minimum number of literals.
– No unique solution
37. 13IDP14- Digital Electronics 37
Algebraic Simplification
Boolean (or Switching) expressions can be
simplified using the following methods:
1. Multiplying out the expression
2. Factoring the expression
3. Combining terms of the expression
4. Eliminating terms in the expression
5. Eliminating literals in the expression
6. Adding redundant terms to the expression