- Boolean algebra uses binary numbers (0 and 1) and logical operations (AND, OR, NOT) to analyze and simplify digital circuits.
- It was invented by George Boole in 1854 and represents variables that can be either 1 or 0.
- The document discusses Boolean operations, laws, logic gates, minimization techniques, and representing functions as sums of products.
Water scarcity is the lack of fresh water resources to meet the standard water demand. There are two type of water scarcity. One is physical. The other is economic water scarcity.
Water scarcity is the lack of fresh water resources to meet the standard water demand. There are two type of water scarcity. One is physical. The other is economic water scarcity.
CFD Simulation of By-pass Flow in a HRSG module by R&R Consult.pptxR&R Consult
CFD analysis is incredibly effective at solving mysteries and improving the performance of complex systems!
Here's a great example: At a large natural gas-fired power plant, where they use waste heat to generate steam and energy, they were puzzled that their boiler wasn't producing as much steam as expected.
R&R and Tetra Engineering Group Inc. were asked to solve the issue with reduced steam production.
An inspection had shown that a significant amount of hot flue gas was bypassing the boiler tubes, where the heat was supposed to be transferred.
R&R Consult conducted a CFD analysis, which revealed that 6.3% of the flue gas was bypassing the boiler tubes without transferring heat. The analysis also showed that the flue gas was instead being directed along the sides of the boiler and between the modules that were supposed to capture the heat. This was the cause of the reduced performance.
Based on our results, Tetra Engineering installed covering plates to reduce the bypass flow. This improved the boiler's performance and increased electricity production.
It is always satisfying when we can help solve complex challenges like this. Do your systems also need a check-up or optimization? Give us a call!
Work done in cooperation with James Malloy and David Moelling from Tetra Engineering.
More examples of our work https://www.r-r-consult.dk/en/cases-en/
About
Indigenized remote control interface card suitable for MAFI system CCR equipment. Compatible for IDM8000 CCR. Backplane mounted serial and TCP/Ethernet communication module for CCR remote access. IDM 8000 CCR remote control on serial and TCP protocol.
• Remote control: Parallel or serial interface.
• Compatible with MAFI CCR system.
• Compatible with IDM8000 CCR.
• Compatible with Backplane mount serial communication.
• Compatible with commercial and Defence aviation CCR system.
• Remote control system for accessing CCR and allied system over serial or TCP.
• Indigenized local Support/presence in India.
• Easy in configuration using DIP switches.
Technical Specifications
Indigenized remote control interface card suitable for MAFI system CCR equipment. Compatible for IDM8000 CCR. Backplane mounted serial and TCP/Ethernet communication module for CCR remote access. IDM 8000 CCR remote control on serial and TCP protocol.
Key Features
Indigenized remote control interface card suitable for MAFI system CCR equipment. Compatible for IDM8000 CCR. Backplane mounted serial and TCP/Ethernet communication module for CCR remote access. IDM 8000 CCR remote control on serial and TCP protocol.
• Remote control: Parallel or serial interface
• Compatible with MAFI CCR system
• Copatiable with IDM8000 CCR
• Compatible with Backplane mount serial communication.
• Compatible with commercial and Defence aviation CCR system.
• Remote control system for accessing CCR and allied system over serial or TCP.
• Indigenized local Support/presence in India.
Application
• Remote control: Parallel or serial interface.
• Compatible with MAFI CCR system.
• Compatible with IDM8000 CCR.
• Compatible with Backplane mount serial communication.
• Compatible with commercial and Defence aviation CCR system.
• Remote control system for accessing CCR and allied system over serial or TCP.
• Indigenized local Support/presence in India.
• Easy in configuration using DIP switches.
Sachpazis:Terzaghi Bearing Capacity Estimation in simple terms with Calculati...Dr.Costas Sachpazis
Terzaghi's soil bearing capacity theory, developed by Karl Terzaghi, is a fundamental principle in geotechnical engineering used to determine the bearing capacity of shallow foundations. This theory provides a method to calculate the ultimate bearing capacity of soil, which is the maximum load per unit area that the soil can support without undergoing shear failure. The Calculation HTML Code included.
Immunizing Image Classifiers Against Localized Adversary Attacksgerogepatton
This paper addresses the vulnerability of deep learning models, particularly convolutional neural networks
(CNN)s, to adversarial attacks and presents a proactive training technique designed to counter them. We
introduce a novel volumization algorithm, which transforms 2D images into 3D volumetric representations.
When combined with 3D convolution and deep curriculum learning optimization (CLO), itsignificantly improves
the immunity of models against localized universal attacks by up to 40%. We evaluate our proposed approach
using contemporary CNN architectures and the modified Canadian Institute for Advanced Research (CIFAR-10
and CIFAR-100) and ImageNet Large Scale Visual Recognition Challenge (ILSVRC12) datasets, showcasing
accuracy improvements over previous techniques. The results indicate that the combination of the volumetric
input and curriculum learning holds significant promise for mitigating adversarial attacks without necessitating
adversary training.
3. 2
Boolean Algebra Summary
• Boolean Algebra is used to analyze and simplify the digital (logic) circuits. It
uses only the binary numbers i.e. 0 and 1. It is also called as Binary
Algebra or logical Algebra.
• Boolean algebra was invented by George Boole in 1854. A variable whose
value can be either 1 or 0 is called a Boolean variable.
• AND, OR, and NOT are the basic Boolean operations.
• We can express Boolean functions with either an expression or a truth table.
• Now, we’ll look at how Boolean algebra can help simplify expressions,
which in turn will lead to simpler circuits.
4. Rules in Boolean Algebra
Following are the important rules used in Boolean algebra.
1. Variable used can have only two values. Binary 1 for HIGH and Binary 0 for LOW.
2. Complement of a variable is represented by an over bar (-). Thus, complement
of variable B is represented as . Thus if B = 0 then = 1 and B = 1 then = 0.
3. OR ing of the variables is represented by a plus (+) sign between them. For
example OR ing of A, B, C is represented as A + B + C.
4. Logical AND ing of the two or more variable is represented by writing a dot
between them such as A.B.C. Sometime the dot may be omitted like ABC.
5. Boolean Algebra Summary
• Recall that the two binary values have different names:
– True/False
– On/Off
– Yes/No
– 1/0
• We use 1 and 0 to denote the two values.
• The three basic logical operations are:
– AND
– OR
– NOT
• AND is denoted by a dot (·).
• OR is denoted by a plus (+).
• NOT is denoted by an overbar ( ¯ ), a single quote mark (') after
6. Boolean Laws
There are six types of Boolean Laws.
Commutative law
• Any binary operation which satisfies the following expression is referred to as
commutative operation.
• Commutative law states that changing the sequence of the variables does not have any
effect on the output of a logic circuit.
7. Associative law
•This law states that the order in which the logic operations are performed is
irrelevant as their effect is the same.
Distributive law
•Distributive law states the following condition.
Boolean Laws
8. AND law
•These laws use the AND operation. Therefore they are called as AND laws.
OR law
•These laws use the OR operation. Therefore they are called as OR laws.
Boolean Laws
9. INVERSION law
•This law uses the NOT operation. The inversion law states that double inversion of a
variable results in the original variable itself.
Boolean Laws
10. Proofs
A 0 A.0=0
0 0 0
1 0 0
AND law
1. A.0=0
A 1 A.1=A
0 1 0
1 1 1
2. A.1=A
A A A.A=A
0 0 0
1 1 1
3. A.A=A
A A A.A=0
0 1 0
1 0 0
4. A.A=0
11. Proofs
A 0 A+0=A
0 0 0
1 0 1
OR law
1. A+0=A
A 1 A+1=1
0 1 1
1 1 1
2. A+1=1
A A A+A=A
0 0 0
1 1 1
3. A+A=A
A A A+A=1
0 1 1
1 0 1
4. A+A=1
13. •Logic gates are the basic building blocks of any digital system.
• It is an electronic circuit having one or more than one input and only one
output.
•The relationship between the input and the output is based on a certain logic.
Based on this, logic gates are named as AND gate, OR gate, NOT gate etc.
Logic gates
AND Gate
A circuit which performs an AND operation is shown in figure. It has n input
(n >= 2) and one output.
15. OR Gate
A circuit which performs an OR operation is shown in figure. It has n input (n >= 2)
and one output.
Logic diagram
Truth Table
16. NOT Gate
NOT gate is also known as Inverter. It has one input A and one output Y.
Logic diagram Truth Table
17. NAND Gate
A NOT-AND operation is known as NAND operation. It has n input (n >= 2) and one output.
Logic diagram Truth Table
18. NOR Gate
A NOT-OR operation is known as NOR operation. It has n input (n >= 2) and one output.
Logic diagram
Truth Table
19. XOR Gate
XOR or Ex-OR gate is a special type of gate. It can be used in the half adder, full adder and subtractor.
The exclusive-OR gate is abbreviated as EX-OR gate or sometime as X-OR gate. It has n input (n >= 2)
and one output.
Logic diagram
Truth Table
20. XNOR Gate
XNOR gate is a special type of gate. It can be used in the half adder, full adder and subtractor. The
exclusive-NOR gate is abbreviated as EX-NOR gate or sometime as X-NOR gate. It has n input (n >= 2)
and one output.
Logic diagram
Truth Table
21. De Morgan's Theorems
De Morgan has suggested two theorems which are extremely useful in Boolean Algebra. The two
theorems are discussed below.
Theorem 1
• The left hand side (LHS) of this theorem represents a NAND gate with inputs A and B, whereas
the right hand side (RHS) of the theorem represents an OR gate with inverted inputs.
• This OR gate is called as Bubbled OR.
24. Theorem 2
•The LHS of this theorem represents a NOR gate with inputs A and B, whereas the RHS
represents an AND gate with inverted inputs.
•This AND gate is called as Bubbled AND.
27. •This theorem states that the dual of the Boolean function
is obtained by interchanging the logical AND operator with
logical OR operator and zeros with ones.
•For every Boolean function, there will be a corresponding
Dual function.
Duality principle
28. Group1 Group2
x + 0 = x x.1 = x
x + 1 = 1 x.0 = 0
x + x = x x.x = x
x + x’ = 1 x.x’ = 0
x + y = y + x x.y = y.x
x + y+zy+z = x+yx+y + z x.y.zy.z = x.yx.y.z
x.y+zy+z = x.y + x.z x + y.zy.z = x+yx+y.x+z
In each row, there are two Boolean equations and they are dual to each other. We can
verify all these Boolean equations of Group1 and Group2 by using duality theorem.
Duality principle
29. Consensus Theorem
Theorem1. AB+ A’C + BC = AB + A’C
Theorem2. (A+B). (A’+C).(B+C) =(A+B).( A’+C)
•The BC term is called the consensus term and is redundant.
•The consensus term is formed from a PAIR OF TERMS in which a variable (A) and its complement
(A’) are present;
•the consensus term is formed by multiplying the two terms and leaving out the selected variable
and its complement
36. Problem
Minimize the following Boolean expression using Boolean identities −
F(A,B,C)=A′B+BC′+BC+AB′C′
Given F(A,B,C)=A′B+BC′+BC+AB′C′
F(A,B,C)=A′B+B(C′+C)+AB′C′
F(A,B,C)=A’B+B.1+AB’C’
= A’B+B+AB’C’ [B.1=B]
= B(A’+1)+AB’C’ [A’+1=1]
= B+AB’C’ [Apply distributive law A+BC=(A+B)(A+C)]
= (B+B’)(B+AC’) [B+B’=1]
= B+AC’
37. Problem
Minimize the following Boolean expression using Boolean identities −
F(A,B,C)=(A+B)(A+C)
Given, F(A,B,C)=(A+B)(A+C)
F(A,B,C)=A.A+A.C+B.A+B.C
=A+AC+AB+BC [A.A=A]
= A(1+C+B)+BC [1+Anything=1]
= A+BC
38.
39. • Boolean algebra deals with binary variables and logic operation. A Boolean
Function is described by an algebraic expression called Boolean
expression which consists of binary variables, the constants 0 and 1, and the logic
operation symbols. Consider the following example.
Here the left side of the equation represents the output Y. So we can state equation
no. 1
Boolean Expression ⁄ Function
40. •A truth table represents a table having all combinations of inputs and their
corresponding result.
•It is possible to convert the switching equation into a truth table. For example,
consider the following switching equation.
•The output will be high (1) if A = 1 or BC = 1 or both are 1. The truth table for this
equation is shown by Table (a). The number of rows in the truth table is 2n
where
n is the number of input variables (n=3 for the given equation). Hence there are
23
= 8 possible input combination of inputs.
Truth Table Formation
41.
42. •It is in the form of sum of three terms AB, AC, BC with each individual term is a
product of two variables. Say A.B or A.C etc. Therefore such expressions are
known as expression in SOP form.
•The sum and products in SOP form are not the actual additions or multiplications.
In fact they are the OR and AND functions.
•In SOP form, 0 represents a bar and 1 represents an unbar. SOP form is
represented by Given below is an example of SOP.
Sum of Products (SOP) Form