Boolean Rules

Rules of Boolean Operations

There are a number of rules that can be used to simplify boolean expressions. Simplified expressions are cheaper and easier to implement as fewer logic gates are needed.

Absorption

We can simplify expressions in the following way:
- $X+(X.Y) = X +X = X$
We can only do this if:
- The value outside the brackets must be present within the brackets.
- The operators inside and outside the brackets must be different.
We say that Y has been absorbed.

Commutative

The commutative rule states that values in AND or OR expressions can be swapped without changing the result:
- $X. Y = Y . X$
- $X + Y = Y + X$

Distributive

A value outside of a set of brackets can be distributed between the values within the brackets:
- $X . (Y + Z) = (X . Y) + (X . Z)$
- $X + (Y . Z) = (X + Y) .(X + Z)$

Associative

The associative rule confirms that the order of operators in an expression has no impact on the result:
- $(X + Y) + Z = X + (Y + Z)$
- $(X . Y) .Z= X . (Y . Z)$

Double Negation

The equivalent of any double-negative is a positive:
- $\overline{(\overline{X})} = X$

De Morgan's Law

De Morgan's law is as follows:
- $\overline{X + Y} = \overline{X} . \overline{Y}$
- $\overline{X . Y} = \overline{X} + \overline{Y}$
We can use this law to convert part of an expression so the whole expression only uses one type of operator.
This reduces the cost as only one type of gate is required.

1Components of a Computer

2Software & Software Development

2.1Systems Software

2.1.1Operating Systems

2.1.2Managing Memory

2.1.3Paging

2.1.4Segmentation

2.1.5Device Management & Drivers

2.1.6Interrupts

2.1.7Interrupt Service Routine (ISR)

2.1.8Scheduling

2.1.9Types of Scheduling

2.1.10Types of Operating System

2.1.11BIOS

2.1.12Virtual Machines

2.2Applications Generation

2.2.1Applications Software

2.2.2Utilities

2.2.3Encryption Software

2.2.4Defragmentation Software

2.2.5Data Compression Software

2.2.6Backup Software

2.2.7Open Source Software

2.2.8Proprietary Software

2.2.9Licensing Issues

2.2.10Compilers

2.2.11Interpreters

2.2.12Assemblers

2.2.13Compiling a Program

2.2.14Lexical Analysis

2.2.15Compilation Stages

2.2.16Linkers, Loaders & Libraries

2.3Software Development

2.3.1Algorithmic Thinking

2.3.2Waterfall Lifecycle

2.3.3Waterfall Lifecycle - Strengths & Weaknesses

2.3.4Agile Methodology

2.3.5Agile Methodology - Strengths & Weaknesses

2.3.6Extreme Programming

2.3.7Extreme Programming - Strengths & Weaknesses

2.3.8Spiral Methodology

2.3.9Spiral Methodology - Strengths & Weaknesses

2.3.10Rapid Application Development

2.3.11RAD - Strengths & Weaknesse

2.4Types of Programming Language

2.4.1High Level Programming Languages

2.4.2Low Level Programming Languages

2.4.3Programming Paradigms

2.4.4Procedural Programming Languages

2.4.5Assembly

2.4.6Machine Code

2.4.7Modes of Addressing Memory

2.4.8Object-Oriented Languages

2.4.9Classes

2.4.10Objects

2.4.11Encapsulation

2.4.12Polymorphism

3Exchanging Data

3.1Compression, Encryption & Hashing

3.1.1Compression

3.1.2Run Length Encoding

3.1.3Dictionary Coding

3.1.4Encryption

3.1.5Symmetric Encyrption

3.1.6Hashing

3.2Databases

3.2.1Records

3.2.2Databases

3.2.3Relational Databases

3.2.4Entity Relationship Modelling

3.2.5Managing Databases

3.2.6Normalisation

3.2.7SQL

3.2.8Principles of Data Storage

3.2.9Atomicity, Consistency, Isolation & Durability

3.3Networks

3.4Web Technologies

3.4.1HTML

3.4.2CSS

3.4.3JavaScript

3.4.4Search Engine Indexing

3.4.5PageRank Algorithm

3.4.6Server & Client-Side Processing

4Data Types, Data Structures & Algorithms

4.1Data Types

4.2Data Structures

4.2.13D Arrays

4.2.2Linked List

4.2.3Queues

4.2.4Graphs

4.2.5Hash Tables

4.2.6Stacks

4.2.7Trees

4.2.8Binary Search Trees

4.3Boolean Algebra

4.3.1Binary Systems

4.3.2Logic Circuits

4.3.3Boolean Operators

4.3.4Evaluating Expressions

4.3.5Boolean Logic

4.3.6Karnaugh Maps

4.3.7Boolean Identities

4.3.8Boolean Rules

4.3.9Flip Flops

4.3.10Adder Circuits

5Legal, Moral, Cultural & Ethical Issues

5.1Computing Related Legislation

5.1.1Data Protection Act (1998)

5.1.2Computer Misuse Act (1990)

5.1.3Copyright Designs & Patents Act (1988)

5.1.4Creative Commons Licensing

5.1.5Regulation of Investigatory Powers Act (2000)

5.2Moral & Ethical Issues

5.2.1Online Activity Tracking

5.2.2Censorship

5.2.3Positive Cultural Impacts

5.2.4Negative Cultural Impacts

5.2.5E-Waste

5.2.6Energy Consumption

5.2.7Positive Environmental Impact

5.2.8Layout, Colour Paradigms & Character Sets

5.2.9Computers in the Workplace

5.2.10Automated Decision-Making

5.2.11Artificial Intelligence

5.2.12Monitoring Behaviour

5.2.13Analysing Personal Information

5.2.14Piracy & Offensive Communication

6Elements of Computational Thinking

6.1Thinking Abstractly

6.1.1Abstraction

6.2Thinking Ahead

6.2.1Inputs & Outputs

6.3Thinking Procedurally

6.3.1Decomposition

6.4Thinking Logically

6.4.1Pseudocode

6.4.2Flow Diagrams

6.5Thinking Concurrently

6.5.1Concurrent Processing

7Problem Solving & Programming

7.1Programming Techniques

7.1.1Variables & Constants

7.1.2Comments

7.1.3Inputs & Outputs

7.1.4Subroutines

7.1.5Scope

7.2Programming Construction

7.2.1Integrated Development Environments

7.2.2The Purpose of Testing

7.2.3Types of Testing

7.2.4Test Plans

8Algorithms

8.1Algorithms

8.1.1Interpreting Algorithms

8.1.2Correcting Algorithms

8.1.3Completing Algorithms

8.1.4Sort Algorithms

8.1.5Bubble Sort

8.1.6Insertion Sort

8.1.7Merge Sort

8.1.8Search Algorithms

8.1.9Linear Search

8.1.10Binary Search

8.1.11Quick Sort Algorithm

8.1.12A* Algorithm

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