Floating Point Subtraction

When subtracting floating point binary numbers, it is important to ensure each number is represented with the same level of precision. This means that the exponents must be the same.

Subtraction

The example below shows the subtraction of two normalised 12-bit floating point numbers, with 8-bit mantissas and 4-bit exponents:
- 0.10110000011 − 0.11100000010

Matching exponents

The first step is to ensure the exponents of the two numbers match, by adding 1 to the exponent of the second number (2) to match that of the first (3).
Adding 1 to the exponent of the second number moves the binary point of the mantissa in this number one place to the left:
- 0.11100000010 $\rightarrow$ 0.01110000011

Two's complement

The next step is to find the twos complement of the second number:
- 1.1001000

Add mantissas

The two mantissas can then be added:
- 0.1011000 + 1.1001000 = 0.1000000
Note that the first digit of the two's complement corresponds to -1 in decimal.
Factor this in when you do the addition.

Normalise the result

The result should then be normalised by moving the binary point one place to the left.
That means we add 1 to the exponent:
- 1.00100000100

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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