Floating Points in Binary

Floating Point Representation

Floating point is a method of representing numbers in binary, which makes use of a binary point placed after the ‘most significant bit’ (MSB).

Floating point

A floating point binary number is made up of two parts:
- The mantissa is the main number, containing a binary point after the MSB.
- The exponent determines where the binary point is positioned before the number is read.
If the exponent is negative (i.e. it begins with a ‘1’), the binary point is moved left instead of right.

Converting to denary

After the binary point has been moved, we can read the value of the mantissa.
The denary value of the binary digit to the right of the binary point corresponds to:
- $2^{-1}=\frac{1}{2}$ .
Each subsequent binary digit corresponds to $2^{-2},\,2^{-3},\,2^{-4}$ .. and so on.

Example

The example below is a 12-bit floating point number, with an 8-bit mantissa and a 4-bit exponent:
- 0 . 1 0 1 1 0 0 0 0 0 1 1
The exponent 0011 (which is equal to 3) identifies where the binary point should move in order to read the number.

Example cont.

In this example, the binary point is moved 3 places to the right, which in turn subtracts 3 from the exponent:
- 0 1 0 1 . 1 0 0 0 0 0 0 0
This represents the decimal number 5.5.

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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