Binary Arithmetic

Test yourself

Binary Addition

We can add two binary numbers in exactly the same way as denary numbers.

Adding two digits

If we add 0 + 0 we get 0.
If we add 1 + 0 (or 0 + 1) we get 1.
If we add 1 + 1, then we cannot use the symbol 2. So we need to carry the 1 and put 0 in the current place.

Adding in a third bit

It might be the case that we have 1 + 1 and also a 1 carried over from the previous column.
If this is the case, then we carry the 1 and have 1 left over.
- So we carry 1 and put 1 in the current place.

Overflow errors

Binary numbers are stored as a fixed length.
If a number is carried past the last place column, then this is called an overflow error.
Overflow errors can lead to inaccurate results and software crashes.

Binary Shifts

A binary shift is a technique for performing multiplication or division on a binary number.

Binary shift

In a binary shift, each digit is moved one column to the left or the right.
Extra 0 bits are added to the start or end of the binary number to fill any missing spaces.

Left binary shift

In a left binary shift, each digit is moved one place to the left.
- This has the effect of multiplying the number by two.
You must take care, when performing a left shift, that there is no overflow error (where we run out of space to store the last digit of the number).

Right binary shift

In a right binary shift, each digit is moved one place to the right.
- This has the effect of dividing the number by two.
You must take care when performing a right shift that no data is shifted off the right hand side. This can cause a loss of accuracy.

1Computer Systems

1.1Systems Architecture

1.1.1Architecture Introduction

1.1.2Von Neumann Architecture

1.1.3Fetch-Execute Cycle

1.1.4Factors Affecting CPU Performance

1.1.5Elements of Computer Systems

1.1.6Exam-Style Questions - Von Neumann Architecture

1.2Memory & Storage

1.3Computer Networks, Connections & Protocols

1.4Network Security

1.4.1Forms of Attack

1.4.2Malware

1.4.3Social Engineering

1.4.4Phishing

1.4.5Common Active Attacks

1.4.6Information Security

1.4.7SQL Injection

1.4.8Network Administration

1.4.9Protecting Against Malware

1.4.10Authentication & Passwords

1.4.11Encryption

1.4.12End of Topic Test - Networks

1.5Systems Software

1.5.1Types of System Software

1.5.2Operating Systems

1.5.3Operating System Managers

1.5.4File Management

1.5.5Device Management

1.5.6User Management

1.5.7Utility Software: Encryption & Defragmentation

1.5.8Utility Software: Data Compression & Backup

1.6Ethical, Legal, Cultural & Environmental Concern

1.6.1Open Source vs Proprietary Software

1.6.2Licensing Issues

1.6.3Ethical Issues

1.6.4Ethical Issues 2

1.6.5Exam-Style Questions - Ethical Issues

1.6.6Legal Issues

1.6.7Legal Issues 2

1.6.8Freedom of Information Act (2000)

1.6.9Cultural Issues

1.6.10Environmental Issues

1.6.11Positive Environmental Impact

1.6.12Privacy Issues

1.6.13Stakeholders

1.6.14End of Topic Test - Software & Issues

2Computational Thinking, Algorithms and Programming

2.1Algorithms

2.1.1Computational Thinking

2.1.2Algorithmic Thinking

2.1.3Pseudocode & Flow Diagrams

2.1.4Interpreting & Correcting Algorithm

2.1.5Completing Algorithms

2.1.6Search Algorithms

2.1.7Binary Search

2.1.8Overview of Sort Algorithms

2.1.9Bubble Sort & Insertion Sort

2.1.10Merge Sort

2.1.11Exam-Style Questions - Sorting Algorithms

2.2Programming Fundamentals

2.2.1Fundamentals

2.2.2Program Flow 1

2.2.3Program Flow 2

2.2.4Arithmetic & Relational Operators

2.2.5Boolean Operators

2.2.6Data Types

2.2.7Arrays

2.2.8Strings

2.2.9File Handling

2.2.10Structuring Data

2.2.11End of Topic Test - Programming

2.2.12Exam-Style Questions - Translation

2.3Producing Robust Programs

2.3.1Defensive Design Considerations

2.3.2Defensive Design Considerations 2

2.3.3Maintainability

2.3.4Testing

2.3.5Test Plans

2.3.6Error Types

2.3.7End of Topic Test - Programming

2.3.8Exam-Style Questions - Testing

2.4Boolean Logic

2.4.1Computational Logic

2.4.2Boolean Logic

2.4.3Boolean Operators

2.4.4Grade 9 - Logic

2.5Programming Languages & IDEs

2.5.1High-Level vs Low-Level Languages

2.5.2Translation - Compliers & Interpreter

2.5.3Translation - Assemblers

2.5.4Integrated Development Environments

2.5.5Exam-Style Questions - Translation

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