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- Тип файла:ppt / pptx (powerpoint)
- Всего слайдов:56 слайдов
- Для класса:1,2,3,4,5,6,7,8,9,10,11
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Слайды и текст к этой презентации:
№3 слайд
Содержание слайда: Binary Logic and Gates
Binary variables take on one of two values.
Logical operators operate on binary values and binary variables.
Basic logical operators are the logic functions AND, OR and NOT.
Logic gates implement logic functions.
Boolean Algebra: a useful mathematical system for specifying and transforming logic functions.
We study Boolean algebra as a foundation for designing and analyzing digital systems!
№4 слайд
Содержание слайда: Logic Gates
In the earliest computers, switches were opened and closed by magnetic fields produced by energizing coils in relays. The switches in turn opened and closed the current paths.
Later, vacuum tubes that open and close current paths electronically replaced relays.
Today, transistors are used as electronic switches that open and close current paths.
№11 слайд
Содержание слайда: Problem 1
A system used 3 switches A,B and C; a combination of switches determines whether an alarm, X, sounds:
If switch A or Switch B are in the ON position and if switch C is in the OFF position then a signal to sound an alarm, X is produced.
Convert this problem into a logic statement.
№12 слайд
Содержание слайда: Problem 2
A nuclear power station has a safety system based on three inputs to a logic circuit(network). A warning signal ( S = 1) is produced when certain conditions in the nuclear power station occur based on these three inputs
A warning signal (S=1) will be produced when any of the following occurs.
Either (a) Temperature > 115 C and Cooling water <=120 litres/hour
or (b) Temperature <=115 C and when Reactor pressure > 15 bar
or cooling water <= 120 litres/hour
Draw a logic circuit and truth table to show all the possible situations when the warning signal (S) could be received.
№15 слайд
Содержание слайда: Some Properties of Boolean Algebra
Boolean Algebra is defined in general by a set B that can have more than two values
A two-valued Boolean algebra is also know as Switching Algebra. The Boolean set B is restricted to 0 and 1. Switching circuits can be represented by this algebra.
The dual of an algebraic expression is obtained by interchanging + and · and interchanging 0’s and 1’s.
The identities appear in dual pairs. When there is only one identity on a line the identity is self-dual, i. e., the dual expression = the original expression.
Sometimes, the dot symbol ‘’ (AND operator) is not written when the meaning is clear.
№17 слайд
Содержание слайда: Boolean Algebraic Proof – Example 1
A + A · B = A (Absorption Theorem)
Proof Steps Justification
A + A · B
= A · 1 + A · B Identity element: A · 1 = A
= A · ( 1 + B) Distributive
= A · 1 1 + B = 1
= A Identity element
Our primary reason for doing proofs is to learn:
Careful and efficient use of the identities and theorems of Boolean algebra, and
How to choose the appropriate identity or theorem to apply to make forward progress, irrespective of the application.
№21 слайд
Содержание слайда: Simplification of Boolean Algebra
(A + B)(A + C) = A + BC
This rule can be proved as follows:
(A + B)(A + C) = AA + AC + AB + BC( Distributive law)
= A + AC + AB + BC ( AA = A)
= A( 1 + C) + AB + BC (1 + C = 1)
= A. 1 + AB + BC
= A(1 + B) + BC (1 + B = 1)
= A. 1 + BC ( A . 1 = A)
= A + BC
№27 слайд
Содержание слайда: Simplification-Example
Using Boolean algebra techniques, simplify this expression:
AB + A(B + C) + B(B + C)
Step 1: Apply the distributive law to the second and third terms in the expression, as follows:
AB + AB + AC + BB + BC
Step 2: Apply (BB = B) to the fourth term.
AB + AB + AC + B + BC
Step 3: Apply (AB + AB = AB) to the first two terms.
AB + AC + B + BC
Step 4: Apply (B + BC = B) to the last two terms.
AB + AC + B
Step 5: Apply (AB + B = B) to the first and third terms.
B+AC
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