Representing Numbers

Test yourself

Binary

In everyday life, we use the denary number system. Computers use binary instead.

Denary

In everyday life, we use a denary number system.
We use 10 symbols to represent each digit.
Each digit's place value is multiplied by 10 as we move from right to left.

Binary

Binary is an identical system, except using two symbols for each digit.
Only 1 and 0 are used in binary.
Each digit's place value is multiplied by two as we move from right to left.

Hexadecimal

Hexadecimal uses 16 different symbols for each place.
Hexadecimal uses the digits 0-9 then A-F:
- A = 10 in denary, B = 11 ...
Each digit's place value is multiplied by 16 as we move from right to left.

Sign and Magnitude

Sign and magnitude is a method of differentiating between positive and negative binary numbers

Most significant bit

In sign and magnitude representation, the first bit in any byte is called the ‘most significant bit’ (MSB).
The MSB determines whether it is a positive or a negative number.
- If the MSB is a 0, the number is positive.
- If the MSB is a 1, the number is negative.

Example

For example:
- 00000100 represents the number 4
- 10000100 represents the number -4

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

Jump to other topics