4.3.7

Boolean Identities

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Boolean Identities

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.

AND identities

AND identities

  • A value AND false returns false.
    • X.0=0X. 0 = 0
  • A value AND true returns the value.
    • X.1=XX.1 = X
  • A value AND the same value returns the value.
    • X.X=XX.X = X
  • A value AND NOT the same value returns false.
    • X.X‾=0X.\overline{X} = 0
OR identities

OR identities

  • A value OR false returns the value.
    • X+0=XX + 0 = X
  • A value OR true returns true.
    • X+1=1X + 1 = 1
  • A value OR the same value returns the value.
    • X+X=XX + X = X
  • A value OR NOT the same value returns true.
    • X+X‾=1X +\overline{X} = 1
Example

Example

  • Using the identities, we can simplify the expression:
    • (X.X)+(X+0)(X.X)+(X+0)
    • (X.X)+X(X . X) + X
    • X+XX + X
    • XX
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1

Components of a Computer

1.1

Structure & Function of the Processor

1.1.1Von Neumann Architecture1.1.2Registers1.1.3Buses1.1.4Fetch, Decode, Execute Cycle1.1.5Factors Affecting CPU Performance1.1.6Pipelining1.1.7CPU Architecture
1.2

Types of Processors

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1.3

Input, Output & Storage

1.3.1Elements of Computer Systems1.3.2Types of Computer Systems1.3.3How Magnetic Storage Works1.3.4Properties of Magnetic Storage1.3.5Examples of Magnetic Storage1.3.6How Optical Storage Works1.3.7Properties of Optical Storage1.3.8Examples of Optical Storage1.3.9Types of Optical Disc1.3.10Random Access Memory1.3.11Read Only Memory1.3.12Uses of Flash Memory1.3.13Properties of Flash Memory1.3.14What to do When We Run Out of Memory1.3.15How Virtual Memory Works
2

Software & Software Development

2.1

Systems Software

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2.2

Applications Generation

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2.3

Software Development

2.3.1Algorithmic Thinking2.3.2Waterfall Lifecycle2.3.3Waterfall Lifecycle - Strengths & Weaknesses2.3.4Agile Methodology2.3.5Agile Methodology - Strengths & Weaknesses2.3.6Extreme Programming2.3.7Extreme Programming - Strengths & Weaknesses2.3.8Spiral Methodology2.3.9Spiral Methodology - Strengths & Weaknesses2.3.10Rapid Application Development2.3.11RAD - Strengths & Weaknesse
2.4

Types of Programming Language

2.4.1High Level Programming Languages2.4.2Low Level Programming Languages2.4.3Programming Paradigms2.4.4Procedural Programming Languages2.4.5Assembly2.4.6Machine Code2.4.7Modes of Addressing Memory2.4.8Object-Oriented Languages2.4.9Classes2.4.10Objects2.4.11Encapsulation2.4.12Polymorphism
3

Exchanging Data

3.1

Compression, Encryption & Hashing

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3.2

Databases

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3.3

Networks

3.3.1The Benefits of Networks3.3.2Network Performance3.3.3Types of Networks3.3.4Network Protocols3.3.5Transmission Protocols3.3.6What is the Internet?3.3.7Uniform Resource Locators3.3.8Domain Name Service3.3.9Web Hosting3.3.10Layering Concepts3.3.11TCP &. OSI Models3.3.12The Advantages of Layering3.3.13What's in a Packet?3.3.14How do Packets get Routed?3.3.15Did my Data Arrive Safely?3.3.16Network Hardware3.3.17Transmission Media3.3.18Firewalls3.3.19Proxies3.3.20Client-Server Model3.3.21Advantages of the Client Server Model3.3.22Disadvantages of the Client Server Model3.3.23Peer-to-Peer Model3.3.24Advantages of the Peer-to-Peer Model3.3.25Disadvantages of the Peer-to-Peer Model
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Web Technologies

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4

Data Types, Data Structures & Algorithms

4.1

Data Types

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4.2

Data Structures

4.2.13D Arrays4.2.2Linked List4.2.3Queues4.2.4Graphs4.2.5Hash Tables4.2.6Stacks4.2.7Trees4.2.8Binary Search Trees
4.3

Boolean Algebra

4.3.1Binary Systems4.3.2Logic Circuits4.3.3Boolean Operators4.3.4Evaluating Expressions4.3.5Boolean Logic4.3.6Karnaugh Maps4.3.7Boolean Identities4.3.8Boolean Rules4.3.9Flip Flops4.3.10Adder Circuits
5

Legal, Moral, Cultural & Ethical Issues

5.1

Computing Related Legislation

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5.2

Moral & Ethical Issues

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6

Elements of Computational Thinking

6.1

Thinking Abstractly

6.1.1Abstraction
6.2

Thinking Ahead

6.2.1Inputs & Outputs
6.3

Thinking Procedurally

6.3.1Decomposition
6.4

Thinking Logically

6.4.1Pseudocode6.4.2Flow Diagrams
6.5

Thinking Concurrently

6.5.1Concurrent Processing
7

Problem Solving & Programming

7.1

Programming Techniques

7.1.1Variables & Constants7.1.2Comments7.1.3Inputs & Outputs7.1.4Subroutines7.1.5Scope
7.2

Programming Construction

7.2.1Integrated Development Environments7.2.2The Purpose of Testing7.2.3Types of Testing7.2.4Test Plans
8

Algorithms

8.1

Algorithms

8.1.1Interpreting Algorithms8.1.2Correcting Algorithms8.1.3Completing Algorithms8.1.4Sort Algorithms8.1.5Bubble Sort8.1.6Insertion Sort8.1.7Merge Sort8.1.8Search Algorithms8.1.9Linear Search8.1.10Binary Search8.1.11Quick Sort Algorithm8.1.12A* Algorithm

Practice questions on Boolean Identities

Can you answer these? Test yourself with free interactive practice on Seneca — used by over 10 million students.

  1. 1
    What is $$Y.Y$$?Multiple choice
  2. 2
    What is $$A+\overline{A}$$?Multiple choice
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Karnaugh Maps

Boolean Rules