4.1.4

Binary Arithmetic

Test yourself

Binary Addition

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

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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.
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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.
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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.

Jump to other topics

1Computational Thinking & Algorithms

1.1Computational Thinking

1.1.1Abstraction Thinking

1.1.2Decomposition Thinking

1.1.3Algorithmic Thinking

1.2Algorithms

1.2.1Algorithms

1.2.2Pseudocode

1.2.3Flow Diagrams

1.2.4Logical Reasoning & Debugging

1.2.5Reading Algorithms

1.2.6Correcting Algorithms

1.2.7Complete the Algorithm

1.2.8Search Algorithms

1.2.9Linear Search

1.2.10Binary Search

1.2.11Sort Algorithms

1.2.12Bubble Sort

1.2.13Insertion Sort

1.2.14End of Topic Test - Algorithms

2Programming

2.1Programming Fundamentals

2.1.1Variables & Constants

2.1.2Comments

2.1.3Input & Output

2.1.4Arithmetic Operators

2.1.5Relational Operators

2.1.6Boolean Operators

2.1.7Sequence

2.1.8Selection

2.1.9Iteration

2.1.10Subroutines

2.1.11Scope

2.1.12Data Types

2.1.13Casting

2.1.14Arrays

2.1.152D Arrays

2.1.16Lists

2.1.172D Lists

2.1.18Strings

2.1.19Syntax Errors

2.1.20Logic Errors

2.1.21Runtime Errors

2.1.22End of Topic Test - Programming

2.2Designing Code

2.2.1Code

2.2.2Programs

2.2.3Writing Your Own Program

2.2.4Designing a ‘Basketball’ Game

2.2.5Turning an Algorithm into an App

2.2.6End of Topic Test - Designing Code

2.3Python

2.3.1Introduction to Python

2.3.2Input

2.3.3Output

2.3.4Casting

2.3.5Type Coercion

2.3.6Selection

2.3.7Iteration

2.3.8Files

2.3.9File Handling

2.3.10Identifiers

2.3.11Whitespace

2.3.12Comments

2.3.13Exceptions

3Hardware & Software

3.1Hardware

3.1.1Elements of Computer Systems

3.1.2Central Processing Unit (CPU)

3.1.3Registers of the Central Processing Unit (CPU)

3.1.4Factors Affecting CPU Performance

3.1.5Fetch-Decode-Execute Cycle

3.1.6Binary Systems

3.1.7Logic Circuits

3.1.8Boolean Logic

3.1.9End of Topic Test - Logic

3.2Software

3.2.1System Software

4Data

4.1Representing Data

4.1.1Binary

4.1.2Converting Binary & Hexadecimal

4.1.3Converting Denary & Hexadecimal

4.1.4Binary Arithmetic

4.1.5Representing Sound

4.1.6Representing Images

4.1.7Character Sets

4.1.8American Standard Code for Information Interchange

4.1.9Unicode

4.1.10End of Topic Test - Representation

5The Internet

5.1Networks

5.1.1Networks

5.1.2Geographical Classification of Networks

5.1.3What is the Internet?

5.1.4The World Wide Web

5.1.5Uniform Resource Locators (URLs)

5.1.6Web Hosting

5.1.7HTML

5.1.8Searching the World Wide Web

5.1.9Good Searching Tips

5.1.10Are You Looking at Reliable Information?

6Online Safety & Security

6.1Protecting Yourself Online

6.1.1Digital Footprints

6.1.2Leaving a Safe Online Footprint

6.1.3Online Safety

6.1.4Malware - Viruses

6.1.5Malware

6.1.6People Online

6.1.7Your Feelings

6.1.8Getting Help

6.2Computing and the Law

6.2.1Data Protection Act (1998)

6.2.2Computer Misuse Act (1990)

6.2.3Freedom of Information Act (2000)

6.2.4Plagiarism

6.2.5Copyright

6.2.6Copyright Designs and Patents Act (1988)

6.2.7Creative Commons Licensing

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Converting Denary & Hexadecimal

Representing Sound