IB Computer Science HL · Year 2 · Lesson 32

Logic gates, truth tables, Karnaugh maps and logic diagrams

Data representation and Boolean logic connect physical binary states to numbers, media, decisions and digital circuits.

Paper 150 minutesA1.2.3 · A1.2.4 · A1.2.5
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Today’s targets

What you need to be able to do

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  • DescribeThe purpose and use of logic gates
  • Construct + analyseAnd analyse truth tables
  • ConstructLogic diagrams
A1.2.3A1.2.4A1.2.5
Paper 1 lensMatch the depth of every response to the command term. Previously learned content can move quickly, but retrieval must still be accurate.
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Retrieve

Rapid Recall Deck

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Say the answer aloud before flipping. Mark secure knowledge quickly and spend time on the gaps.

  • When does an AND gate output 1?: Only when all of its required inputs are 1.
  • When does an OR gate output 1, and when does XOR output 1?: OR outputs 1 when at least one input is 1; XOR outputs 1 when the inputs differ (for two inputs).
  • What do NOT, NAND, NOR, and XNOR do?: NOT inverts one input; NAND is NOT-AND; NOR is NOT-OR; XNOR outputs 1 when two inputs are the same.
  • What is a truth table used for?: To show the output produced for every relevant combination of Boolean inputs.
  • How is a Boolean expression related to a logic circuit?: Each Boolean operator corresponds to a gate, so an expression can be represented as a connected logic diagram and vice versa.
  • What is a Karnaugh map used for?: To group output patterns from a truth table and simplify a Boolean expression.
  • Why simplify a Boolean expression or logic diagram?: A simpler equivalent design can use fewer operations/gates, reducing complexity while preserving the same outputs.
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A1.2.3 + A1.2.4 · Learn

Core knowledge and application

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A1.2.3Describe

The purpose and use of logic gates

Data representation and Boolean logic connect physical binary states to numbers, media, decisions and digital circuits.

Exam moveGive a detailed, accurate account of what happens or what something is like.
Required detail 1Purpose/use of logic gates
Required detail 2Functions/applications of logic gates in computer systems
Required detail 3Role of logic gates in binary computing
Required detail 4Boolean operators: AND, OR, NOT, NAND, NOR, XOR, XNOR

Explain it without notes

Describe: The purpose and use of logic gates in the context of a digital access-control circuit and data-encoding task.

  • Purpose/use of logic gates
  • Functions/applications of logic gates in computer systems
  • Role of logic gates in binary computing
  • Boolean operators: AND, OR, NOT, NAND, NOR, XOR, XNOR
A1.2.4Construct + analyse

And analyse truth tables

Data representation and Boolean logic connect physical binary states to numbers, media, decisions and digital circuits.

Exam moveBuild the required representation or solution, then interpret it accurately.
Required detail 1Truth tables to predict the output of simple logic circuits
Required detail 2Truth tables to determine outputs from inputs for a problem description
Required detail 3Truth tables and their relationship to a Boolean expression, with inputs and outputs
Required detail 4Truth tables derived from logic diagrams to aid the simplification of logical expressions
Required detail 5Karnaugh maps and algebraic simplification to simplify output expressions
Assessment boundaryFull truth tables up to 3 inputs; Karnaugh maps up to 3 variables. if De Morgan/other algebraic laws are required, the laws are provided in the question.

Explain it without notes

Construct + analyse: And analyse truth tables in the context of a digital access-control circuit and data-encoding task.

  • Truth tables to predict the output of simple logic circuits
  • Truth tables to determine outputs from inputs for a problem description
  • Truth tables and their relationship to a Boolean expression, with inputs and outputs
  • Truth tables derived from logic diagrams to aid the simplification of logical expressions
  • Karnaugh maps and algebraic simplification to simplify output expressions
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A1.2.5 · Learn

Core knowledge and application

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A1.2.5Construct

Logic diagrams

Data representation and Boolean logic connect physical binary states to numbers, media, decisions and digital circuits.

Exam moveProduce the required code, diagram, query, model or representation accurately.
Required detail 1Logic diagrams to demonstrate how logic gates are connected and interact in a circuit
Required detail 2Use of standard gate symbols for AND, OR, NOT, NAND, NOR, XOR and XNOR gates
Required detail 3Inputs processed diagrammatically to produce outputs
Required detail 4Combinations of these gates to perform more complex logical operations
Required detail 5Boolean algebra rules to simplify complex logic diagrams and expressions
Assessment boundaryIf De Morgan/other algebraic laws are required for algebraic simplification, the laws are provided in the question. (The published Guide labels this point “A.1.2.5”; normalized here as A1.2.5.)

Explain it without notes

Construct: Logic diagrams in the context of a digital access-control circuit and data-encoding task.

  • Logic diagrams to demonstrate how logic gates are connected and interact in a circuit
  • Use of standard gate symbols for AND, OR, NOT, NAND, NOR, XOR and XNOR gates
  • Inputs processed diagrammatically to produce outputs
  • Combinations of these gates to perform more complex logical operations
  • Boolean algebra rules to simplify complex logic diagrams and expressions
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Worked example · A1.2.3–A1.2.5

Gate symbols, truth tables, Karnaugh maps and logic diagrams

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Standard gate symbols

AND
OR
NOT
NAND
NOR
XOR
XNOR

Truth table example

For F = (A AND B) OR NOT C:

A
B
C
F
0
0
0
1
0
0
1
0
0
1
0
1
0
1
1
0
1
0
0
1
1
0
1
0
1
1
0
1
1
1
1
1

Use the expression or a logic diagram to determine each row systematically.

Three-variable Karnaugh-map example

If F(A,B,C) = Σm(4,5,6,7), all four cells in the A=1 row are grouped, so the simplified output is F = A.

A \ BC
00
01
11
10
0
0
0
0
0
1
1
1
1
1

Logic-diagram path

A, B
→
AND
→
OR
→
F
C
→
NOT
↗

Boolean algebra can simplify an expression before rebuilding a simpler circuit. If a question requires a specific algebraic law such as De Morgan’s law, the law is supplied.

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Apply

Transfer to a new scenario

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ScenarioA digital access-control circuit and data-encoding task needs a design or technical decision related to today’s topic. Explain what matters and why.
  • Purpose/use of logic gates
  • Functions/applications of logic gates in computer systems
  • Truth tables to predict the output of simple logic circuits
  • Truth tables to determine outputs from inputs for a problem description
  • Logic diagrams to demonstrate how logic gates are connected and interact in a circuit
  • Use of standard gate symbols for AND, OR, NOT, NAND, NOR, XOR and XNOR gates
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Exam lens

Paper 1 practice

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Build the response before checking notesUse precise terminology and match the required depth.
  1. Describe: The purpose and use of logic gates in the context of a digital access-control circuit and data-encoding task.
  2. Construct + analyse: And analyse truth tables in the context of a digital access-control circuit and data-encoding task.
  3. Construct: Logic diagrams in the context of a digital access-control circuit and data-encoding task.
Self-checkAnswer the exact command term. For explain, include mechanism/reason; for compare, pair criteria; for discuss/evaluate/justify, build supported reasoning and a conclusion.
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Homework

Finish the learning cycle

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IA — main task

Continue Criterion D development. Keep code readable, record meaningful implementation decisions, and maintain testing/evidence notes as you work.

Syllabus — short

Complete one targeted Paper 2/Paper 1 retrieval task from today’s lesson.

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End of Lesson 32.