2.4.3

Truth Tables

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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?

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

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

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

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.
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1

Computer Systems

1.1

Data Representation

1.1.1Binary Numbers1.1.2Negative Binary Numbers1.1.3Hexadecimal1.1.4Using Hexadecimal1.1.5Converting Binary & Hexadecimal1.1.6Converting Denary & Hexadecimal1.1.7Capacity1.1.8Calculating Capacity Requirements1.1.9Binary in Computer Systems1.1.10Data Compression1.1.11Run Length Encoding1.1.12File Formats
1.2

Data Transmission

1.2.1Packet Switching1.2.2Data Transmission1.2.3Universal Serial Bus (USB)1.2.4Parity Check1.2.5Checksum & Echo Checks1.2.6Encryption
1.3

Hardware

1.3.1Elements of Computer Systems1.3.2Types of Computer System1.3.3Von Neumann Architecture1.3.4The Fetch, Decode, Execute Cycle1.3.5Factors Affecting CPU Performance1.3.6Computational Logic1.3.7Input Devices1.3.82D & 3D Scanners1.3.9Code Readers1.3.10Solid State Storage1.3.11Magnetic Storage1.3.12Examples of Magnetic Storage1.3.13Optical Storage1.3.14Examples of Optical Storage1.3.15Types of Optical disk1.3.16Storage Requirements1.3.17Translation - Compilers1.3.18Translation - Interpreters1.3.19Translation - Assemblers1.3.20Acoustic Sensors1.3.21Flow Sensors1.3.22Gas Sensors1.3.23Humidity Sensors1.3.24Infrared Sensors1.3.25Level Sensors1.3.26Light Sensors1.3.27Magnetic Field Sensors1.3.28Moisture Sensors1.3.29pH Sensors1.3.30Pressure Sensors1.3.31Proximity Sensors1.3.32Temperature Sensors1.3.33Network Hardware
1.4

Software

1.4.1Operating Systems1.4.2Interrupts1.4.3High-Level Languages1.4.4Low-Level Languages
1.5

The Internet & its Uses

1.5.1The Internet1.5.2Uniform Resource Locators (URLs)1.5.3DNS1.5.4HTML1.5.5Cookies1.5.6Web Hosting1.5.7Digital Currency
1.6

Cyber Security

1.6.1Forms of Attack1.6.2Penetration Testing1.6.3Types of Malware1.6.4How Malware Spreads1.6.5Protecting Against Malware1.6.6Information Security1.6.7Structured Query Language (SQL) Injection1.6.8Firewalls1.6.9Authentication: User Access Levels1.6.10Authentication: Passwords1.6.11Social Engineering1.6.12Phishing1.6.13Denial of Service Attacks
1.7

Automated & Emerging Technologies

1.7.1Automated Systems1.7.2Robotics1.7.3Artificial Intelligence
2

Algorithms, Programming & Logic

2.1

Algorithm Design & Problem Solving

2.1.1Computational Thinking - Abstraction2.1.2Computational Thinking - Decomposition2.1.3Computational Thinking - Algorithmic Thinking2.1.4Pseudocode2.1.5Flow Diagrams2.1.6Interpreting, Correcting & Completing Algorithm2.1.7Correcting Algorithms2.1.8Completing Algorithms2.1.9Testing2.1.10Types of Testing2.1.11Test Plans2.1.12Validation & Sanitation2.1.13Authentication & Contingencies
2.2

Programming

2.2.1Programming Fundamentals - Variables & Constants2.2.2Programming Fundamentals - Comments2.2.3Programming Fundamentals - Input & Output2.2.4Data Types2.2.5Casting2.2.6Controlling Program Flow - Sequence2.2.7Controlling Program Flow - Selection2.2.8Controlling Program Flow - Iteration2.2.9Modularity - Subroutines2.2.10Modularity - Scope2.2.11Arrays
2.3

Databases

2.3.1Structuring Data - Records2.3.2Structuring Data - Databases2.3.3SQL
2.4

Boolean Logic

2.4.1Binary Systems2.4.2Logic Circuits2.4.3Truth Tables2.4.4Evaluating Expressions2.4.5Boolean Operators2.4.6End of Topic Test - Logic

Practice questions on Truth Tables

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  1. 1
    What is the purpose of a truth table?Multiple choice
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Logic Circuits

Evaluating Expressions