Boolean Logic

Test yourself

Boolean Operators

Boolean operators perform logical operations on boolean variables and always return another boolean variable.

Illustrative background for AND ?? "content

AND

AND evaluates to True (1) if and only if both operands are True (1).
'.' is the symbol for the AND operator.

Illustrative background for OR ?? "content

OR

OR evaluates to True (1) if any of the two operands are True (1).
'+' is the symbol for the OR operator.

NOT (negation)

NOT negates a logical value.
The symbol for the NOT operator is a line above the variable.
For example, NOT $A$ is written as $\overline{A}$ .

Illustrative background for XOR ?? "content

XOR

XOR means 'exclusive OR'.
The symbol for the XOR operator is $\bigoplus$ .

NAND

NAND means NOT AND.
$A$ NAND $B$ is written as $\overline{A.B}$ .

Illustrative background for NOR ?? "content

NOR

NOR means NOT OR.
$A$ NOR $B$ is written as $\overline{A+B}$ .

Evaluating Expressions

Logic gates can be combined to form logic circuits that process complex logical statements such as A AND (B OR C).

Evaluating boolean expressions

To evaluate a boolean expression, you should substitute all of the values in for the variables and then use the definitions of the different boolean functions to simplify it one step at a time.

Order of evaluation

You should evaluate any expression in brackets first, for example:
- NOT(True OR False).
- NOT(True).
- False.

Truth tables

Another method of evaluating an expression is using a truth table.
A truth table shows every possible combination of inputs and the resulting output.
The truth table shows the input and output state for each combination.
The table can then be used to look up the output.

Defining Problems Using Boolean Logic

It is possible to describe the various outcomes of particular scenarios using boolean logic. The outcomes can then be interpreted using logic gates in an electronic circuit.

Example 1

In order to pass an online course, students must achieve at least 75% in both assessments A and B.

Booelan logic

When approaching a problem like this, truth tables help to identify the possible outcomes.
Whether or not a student passed can be expressed as:
- $P = A.B$

Example 2

A reef supplement should be added if the calcium level drops below 400 ppm or the magnesium drops below 1300 ppm, and the temperature of the water is 24°C.

Booelan logic

Whether or not the supplement is added can be expressed as:
- $D = (C + M).T$

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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