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.

1Components of a Computer

1.1Structure & Function of the Processor

1.1.1Structure of the CPU

1.1.2Fetch, Decode, Execute Cycle

1.1.3Factors Affecting CPU Performance

1.1.4CPU Architecture

1.2Types of Processors

1.2.1CISC & RISC

1.2.2Multicore & Parallel Cores

1.3Input, Output & Storage

1.3.1Computer Systems

1.3.2Magnetic Storage

1.3.3Optical Storage

1.3.4Types of Optical Storage

1.3.5Types of Memory

1.3.6Flash Memory

1.3.7Virtual Memory

2Software & Software Development

3Exchanging Data

4Data Types, Data Structures & Algorithms

4.1Data Types

4.1.1Data Types

4.1.2Arrays & Strings

4.1.3Representing Numbers

4.1.4Binary Arithmetic

4.1.5Hexadecimal

4.1.6Converting Binary Numbers

4.1.7Floating Points in Binary

4.1.8Floating Point Arithmetic

4.1.9Bitwise Manipulation

4.1.10Character Sets

4.2Data Structures

4.2.1Arrays, Linked Lists & Queues

4.2.2Graphs, Hash Tables & Stacks

4.2.3Trees

4.3Boolean Algebra

4.3.1Computational Logic

4.3.2Boolean Logic

4.3.3Karnaugh Maps

4.3.4Boolean Identities

4.3.5Flip Flops & Adder 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 and Patents Act (1988)

5.1.4Regulation of Investigatory Powers Act (2000)

5.2Moral & Ethical Issues

5.2.1Online Activity Tracking

5.2.2Censorship

5.2.3Cultural Issues

5.2.4Environmental Issues

5.2.5Layout, Colour Paradigms & Character Sets

6Elements of Computational Thinking

6.1Thinking Abstractly

6.1.1Abstraction

6.2Thinking Procedurally

6.2.1Decomposition

6.3Thinking Logically

6.3.1Pseudocode & Flow Diagrams

7Problem Solving & Programming

7.1Programming Techniques

7.1.1Programming Fundamentals

7.1.2Modularity

7.2Programming Construction

7.2.1Integrated Development Environments

7.2.2Testing

8Algorithms

8.1Algorithms

8.1.1Interpreting, Correcting & Completing Algorithm

8.1.2Sort Algorithms

8.1.3Insertion & Merge Sort

8.1.4Search Algorithms

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