Truth Tables

A truth table shows all possible input combinations and their corresponding outputs, helping to test and complete logic expressions or circuits systematically.

What is a truth table?

A truth table is used to demonstrate the logic of a logic circuit or a Boolean expression.
It shows the outcome (the 'output') for every possible combination of inputs.
Inputs can only be 0 (false) or 1 (true).
Truth tables are a systematic way to test how logic gates behave and if a logic circuit works as expected.

Building a simple truth table

A truth table has columns for each input and a column for the final output.
- It is common to give the input and output a label (e.g. Input = A, Output = X)
The number of possible input combinations is calculated as 2ⁿ, where ⁿ is the number of inputs.
- For one input, there are 2¹ = 2 combinations (0 and 1).
- For two inputs, there are 2² = 4 combinations (00, 01, 10, 11).
- For three inputs, there are 2³ = 8 combinations.

Completing a truth table

You may be asked to complete a truth table from:
- A problem statement (e.g. “The alarm sounds if both sensors detect movement”)
- A logic expression (e.g. 𝐴⋅𝐵+𝐶)
- A logic circuit (given as a diagram with NOT, OR, NAND or other gates)
For each row, calculate the output by applying the logic operators or gates to the input values.

Three-input truth table example

To complete a truth table, you need to know the specific logic circuit or expression.
With 3 inputs, there are 8 possible combinations of 0s and 1s.
Each row shows one possible input combination and the corresponding output.

1Computer Systems

1.1Data Representation

1.1.1Binary Numbers

1.1.2Negative Binary Numbers

1.1.3Hexadecimal

1.1.4Using Hexadecimal

1.1.5Converting Binary & Hexadecimal

1.1.6Converting Denary & Hexadecimal

1.1.7Capacity

1.1.8Calculating Capacity Requirements

1.1.9Binary in Computer Systems

1.1.10Data Compression

1.1.11Run Length Encoding

1.1.12File Formats

1.2Data Transmission

1.2.1Packet Switching

1.2.2Data Transmission

1.2.3Universal Serial Bus (USB)

1.2.4Parity Check

1.2.5Checksum & Echo Checks

1.2.6Encryption

1.3Hardware

1.4Software

1.4.1Operating Systems

1.4.2Interrupts

1.4.3High-Level Languages

1.4.4Low-Level Languages

1.5The Internet & its Uses

1.5.1The Internet

1.5.2Uniform Resource Locators (URLs)

1.5.3DNS

1.5.4HTML

1.5.5Cookies

1.5.6Web Hosting

1.5.7Digital Currency

1.6Cyber Security

1.6.1Forms of Attack

1.6.2Penetration Testing

1.6.3Types of Malware

1.6.4How Malware Spreads

1.6.5Protecting Against Malware

1.6.6Information Security

1.6.7Structured Query Language (SQL) Injection

1.6.8Firewalls

1.6.9Authentication: User Access Levels

1.6.10Authentication: Passwords

1.6.11Social Engineering

1.6.12Phishing

1.6.13Denial of Service Attacks

1.7Automated & Emerging Technologies

1.7.1Automated Systems

1.7.2Robotics

1.7.3Artificial Intelligence

2Algorithms, Programming & Logic

2.1Algorithm Design & Problem Solving

2.1.1Computational Thinking - Abstraction

2.1.2Computational Thinking - Decomposition

2.1.3Computational Thinking - Algorithmic Thinking

2.1.4Pseudocode

2.1.5Flow Diagrams

2.1.6Interpreting, Correcting & Completing Algorithm

2.1.7Correcting Algorithms

2.1.8Completing Algorithms

2.1.9Testing

2.1.10Types of Testing

2.1.11Test Plans

2.1.12Validation & Sanitation

2.1.13Authentication & Contingencies

2.2Programming

2.2.1Programming Fundamentals - Variables & Constants

2.2.2Programming Fundamentals - Comments

2.2.3Programming Fundamentals - Input & Output

2.2.4Data Types

2.2.5Casting

2.2.6Controlling Program Flow - Sequence

2.2.7Controlling Program Flow - Selection

2.2.8Controlling Program Flow - Iteration

2.2.9Modularity - Subroutines

2.2.10Modularity - Scope

2.2.11Arrays

2.3Databases

2.3.1Structuring Data - Records

2.3.2Structuring Data - Databases

2.3.3SQL

2.4Boolean Logic

2.4.1Binary Systems

2.4.2Logic Circuits

2.4.3Truth Tables

2.4.4Evaluating Expressions

2.4.5Boolean Operators

2.4.6End of Topic Test - Logic

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