3.1.2

Negative Binary Numbers

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Negative Binary Numbers

There exist two systems to express negative numbers in binary.

Sign and magnitude

Sign and magnitude

  • The most significant bit of the binary number is a designated sign bit.
  • If the number is positive then the MSB is set to 0.
  • If the number is negative then the MSB is set to 1.
Sign and magnitude

Sign and magnitude

  • This method allows us to express negative numbers.
  • However, it is very hard to perform arithmetic using this representation.
Two's compliment

Two's compliment

  • The place value of the MSB is made negative.
  • This allows us to express negative numbers by subtracting the largest possible place value, and then adding the difference back on.
Two's compliment

Two's compliment

  • This method is much easier to perform calculations with since we can express subtraction as follows:
    • a - b = a + (-b)
  • This means we do not need a separate subtractor circuit in our processor.
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1

Problem Solving

1.1

Algorithms

1.1.1Algorithm Thinking1.1.2Interpreting Algorithms1.1.3Expressing Algorithms - Pseudocode1.1.4Expressing Algorithms - Flow Charts1.1.5Correcting Algorithms1.1.6Completing Algorithms1.1.7Search Algorithms1.1.8Linear Search1.1.9Binary Search1.1.10Sort Algorithms1.1.11Bubble Sort1.1.12Merge Sort
1.2

Decomposition & Abstraction

1.2.1Computational Thinking - Abstraction1.2.2Computational Thinking - Decomposition1.2.3End of Topic Test - Algorithms
2

Programming

2.1

Develop Code

2.1.1Maintainability2.1.2Comments2.1.3Exceptions2.1.4Syntax Error2.1.5Logic Error2.1.6Runtime Error2.1.7Purpose of Testing2.1.8Test Plans
2.2

Constructs

2.2.1Selection2.2.2Sequence2.2.3Iteration
2.3

Data Types & Structures

2.3.1Variables & Constants2.3.2Scope2.3.3Data Types2.3.4Casting2.3.5Data Structures - Arrays2.3.6Data Structures - 2D Arrays2.3.7Data Structures - Strings2.3.8Data Structures - Records
2.4

Input / Output

2.4.1Input and Output2.4.2Validation and Sanitation2.4.3Files2.4.4File Handling
2.5

Operators

2.5.1Arithmetic Operators2.5.2Relational Operators2.5.3Boolean Operators
2.6

Subprograms

2.6.1Modularity2.6.2End of Topic Test - Programming
3

Data

3.1

Binary

3.1.1Number Bases3.1.2Negative Binary Numbers3.1.3Binary Addition3.1.4Binary Shifts
3.2

Data Representation

3.2.1Representing Text3.2.2ASCII3.2.3Unicode3.2.4Representing Images3.2.5Representing Sound
3.3

Data Storage & Compression

3.3.1Capacity3.3.2Calculating Capacity Requirements3.3.3Data Compression3.3.4Run Length Encoding
3.4

Encryption

3.4.1Encryption3.4.2Caesar Cipher3.4.3Ciphers
3.5

Databases

3.5.1Databases3.5.2End of Topic Test - Data & Representation
4

Computers

4.1

Machines & Computational Modelling

4.1.1Computational Models4.1.2Input-Process-Output Model
4.2

Hardware

4.2.1Elements of Computer Systems4.2.2Types of Computer Systems4.2.3Memory - RAM4.2.4Memory - ROM4.2.5Memory - Cache4.2.6Running Out of Memory4.2.7Virtual Memory4.2.8Magnetic Storage4.2.9Properties of Magnetic Media4.2.10Examples of Magnetic Storage4.2.11Solid State Storage4.2.12Properties of Solid State Media4.2.13Optical Storage4.2.14Properties of Optical Storage4.2.15Examples of Optical Storage4.2.16Types of Optical Disk4.2.17Von Neumann Architecture4.2.18Registers of the Central Processing Unit (CPU)4.2.19Fetch-Decode-Execute Cycle4.2.20Factors Affecting CPU Performance4.2.21The Cloud4.2.22How the Cloud Works4.2.23The Cloud - Pros4.2.24The Cloud - Cons4.2.25End of Topic Test - Hardware
4.3

Logic

4.3.1Binary Systems4.3.2Logic Circuits4.3.3Boolean Logic4.3.4End of Topic Test - Logic
4.4

Software

4.4.1Operating Systems4.4.2User Interface Managetment4.4.3Memory and Process Management4.4.4File Management4.4.5Device Management4.4.6User Management4.4.7Encryption Software4.4.8Defragmentation Software4.4.9Data Compression Software4.4.10Backup Software
4.5

Programming Languages

4.5.1High Level Languages4.5.2Low Level Languages4.5.3Translators - Compilers4.5.4Translators - Interpreters4.5.5Translators - Assemblers4.5.6End of Topic Test - Translation & Representation
5

Communication & The Internet

5.1

Networks

5.1.1Benefits of Networks5.1.2Network Performance5.1.3Types of Network5.1.4Client-Server Model5.1.5Pros of Client-Server Model5.1.6Cons of Client-Server Model5.1.7Peer-to-Peer Model5.1.8Pros of Peer-to-Peer Model5.1.9Cons of Peer-to-Peer Model5.1.10Network Hardware5.1.11Transmission Media5.1.12WiFi5.1.13WiFi Frequency and Channels5.1.14WiFi Encryption5.1.15Network Protocols5.1.16Transmission Protocols5.1.17Web Protocols5.1.18Email Protocols5.1.19Layers5.1.20TCP and OSI Models5.1.21Advantages of Layering5.1.22Topology - Star5.1.23Topology - Mesh5.1.24Topology - Ring5.1.25Topology - Bus5.1.26End of Topic Test - Networks
5.2

Network Security

5.2.1User Access Levels5.2.2Encryption5.2.3Protecting Against Malware5.2.4Firewalls5.2.5Forms of Attack5.2.6Penetration Testing5.2.7Malware5.2.8How Malware Spreads5.2.9Social Engineering5.2.10Protecting Against Social Engineering5.2.11Phishing5.2.12Network Administration5.2.13Network Forensics
5.3

The Internet & the World Wide Web

5.3.1IP Addresses5.3.2Types of IP Address5.3.3MAC Addresses5.3.4Packet Switching5.3.5How Do Packets Get Routed?5.3.6Did My Data Arrive Safely?5.3.7The Internet5.3.8URLs5.3.9DNS5.3.10Web Hosting5.3.11End of Topic Test - Security
6

The Bigger Picture

6.1

Emerging Trends, Issues & Impact

6.1.1E-Waste6.1.2Energy Consumption6.1.3Positive Environmental Impact6.1.4Ethical Issues - The Digital Divide6.1.5Ethical Issues - Net Neutrality6.1.6Ethical Issues - Working Conditions6.1.7Ethical Issues - Censorship6.1.8Online Activity Tracking6.1.9The Internet of Things6.1.10Positive Cultural Impacts6.1.11Negative Cultural Impacts6.1.12Data Protection Act6.1.13Computer Misuse Act6.1.14Copyright Designs and Parents Act6.1.15Creative Commons Licensing6.1.16Freedom of Information Act6.1.17Open Source Software6.1.18Proprietary Software6.1.19Licensing Issues6.1.20End of Topic Test - Software & Issues

Practice questions on Negative Binary Numbers

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

  1. 1
    Which representation is easier to perform maths with?Multiple choice
  2. 2
    Which of the following statements about negative binary numbers are true?True / false
  3. 3
    Negative Binary Number Representations:Fill in the list
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Number Bases

Binary Addition