4.1.4

Binary Arithmetic

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Binary Addition

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

Adding two digits

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

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

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
1

Computational Thinking & Algorithms

1.1

Computational Thinking

1.1.1Abstraction Thinking1.1.2Decomposition Thinking1.1.3Algorithmic Thinking
1.2

Algorithms

1.2.1Algorithms1.2.2Pseudocode1.2.3Flow Diagrams1.2.4Logical Reasoning & Debugging1.2.5Reading Algorithms1.2.6Correcting Algorithms1.2.7Complete the Algorithm1.2.8Search Algorithms1.2.9Linear Search1.2.10Binary Search1.2.11Sort Algorithms1.2.12Bubble Sort1.2.13Insertion Sort1.2.14End of Topic Test - Algorithms
2

Programming

2.1

Programming Fundamentals

2.1.1Variables & Constants2.1.2Comments2.1.3Input & Output2.1.4Arithmetic Operators2.1.5Relational Operators2.1.6Boolean Operators2.1.7Sequence2.1.8Selection2.1.9Iteration2.1.10Subroutines2.1.11Scope2.1.12Data Types2.1.13Casting2.1.14Arrays2.1.152D Arrays2.1.16Lists2.1.172D Lists2.1.18Strings2.1.19Syntax Errors2.1.20Logic Errors2.1.21Runtime Errors2.1.22End of Topic Test - Programming
2.2

Designing Code

2.2.1Code2.2.2Programs2.2.3Writing Your Own Program2.2.4Designing a ‘Basketball’ Game2.2.5Turning an Algorithm into an App2.2.6End of Topic Test - Designing Code
2.3

Python

2.3.1Introduction to Python2.3.2Input2.3.3Output2.3.4Casting2.3.5Type Coercion2.3.6Selection2.3.7Iteration2.3.8Files2.3.9File Handling2.3.10Identifiers2.3.11Whitespace2.3.12Comments2.3.13Exceptions
3

Hardware & Software

3.1

Hardware

3.1.1Elements of Computer Systems3.1.2Central Processing Unit (CPU)3.1.3Registers of the Central Processing Unit (CPU)3.1.4Factors Affecting CPU Performance3.1.5Fetch-Decode-Execute Cycle3.1.6Binary Systems3.1.7Logic Circuits3.1.8Boolean Logic3.1.9End of Topic Test - Logic
3.2

Software

3.2.1System Software
4

Data

4.1

Representing Data

4.1.1Binary4.1.2Converting Binary & Hexadecimal4.1.3Converting Denary & Hexadecimal4.1.4Binary Arithmetic4.1.5Representing Sound4.1.6Representing Images4.1.7Character Sets4.1.8American Standard Code for Information Interchange4.1.9Unicode4.1.10End of Topic Test - Representation
5

The Internet

5.1

Networks

5.1.1Networks5.1.2Geographical Classification of Networks5.1.3What is the Internet?5.1.4The World Wide Web5.1.5Uniform Resource Locators (URLs)5.1.6Web Hosting5.1.7HTML5.1.8Searching the World Wide Web5.1.9Good Searching Tips5.1.10Are You Looking at Reliable Information?
6

Online Safety & Security

6.1

Protecting Yourself Online

6.1.1Digital Footprints6.1.2Leaving a Safe Online Footprint6.1.3Online Safety6.1.4Malware - Viruses6.1.5Malware6.1.6People Online6.1.7Your Feelings6.1.8Getting Help
6.2

Computing and the Law

6.2.1Data Protection Act (1998)6.2.2Computer Misuse Act (1990)6.2.3Freedom of Information Act (2000)6.2.4Plagiarism6.2.5Copyright6.2.6Copyright Designs and Patents Act (1988)6.2.7Creative Commons Licensing

Practice questions on Binary Arithmetic

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  1. 1
    What is overflow?Multiple choice
  2. 2
    Overflow errors can lead to:Fill in the list
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Converting Denary & Hexadecimal

Representing Sound