Digital and Analogue System Design · SHS2 Robotics

Lesson notes

Learning Objectives

Indicator: 2.2.1.LI.2 - Apply Karnaugh Maps to optimise digital systems.

By the end of the lesson, learners can:

Construct a 2-variable and 3-variable Karnaugh Map from a given Truth Table with accurate cell placement.
Group adjacent 1s in a K-Map correctly, following the rules of adjacency (including wrapping around edges).
Derive a simplified Boolean expression from grouped K-Map cells and verify it produces the same output as the original expression.
Apply the full K-Map optimisation process (Truth Table to K-Map to simplified expression) to a practical automation problem presented as a narrative.
Justify why a simplified circuit is preferable to an unsimplified one in terms of cost, power consumption, and component count.

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Curriculum details

Strand: Robot Design Methodologies (Strand 2)
Sub-strand: Digital and Analogue System Design (2.1)
Content standard: 2.2.1.CS.1 - 2.2.1.CS.1 Demonstrate Understanding of Digital Systems and Logic Design principles. 2.2.1.LO.1 Use boolean algebra to define automation solutions and apply Karnaugh Maps to simplify and optimise boolean-defined combinational digital systems.
Indicator: 2.2.1.LI.2 - Apply Karnaugh Maps to optimise digital systems.
Suggested placement: Semester 2, Week 2 (Week 22 of the year)
Our suggestion, laid out in curriculum order across three terms of twelve weeks. NaCCA does not fix the week, so follow your school's scheme of learning.
Curriculum reference: NaCCA curriculum document, p. 103

Exemplars (from the NaCCA curriculum)

Initiating Talk for Learning: Discuss Karnaugh Maps and their application for digital circuit optimisation using working examples.

Project-Based Learning: Task learners in small mixed-ability/gender groups to follow processes in designing and optimising combinational circuits for defined problems (as a narrative). The following steps should be evident in the design process: v Brainstorm and write out functional requirements from the narrative

v Identify the required number of inputs and outputs

v Translate the functional requirements into a Truth Table

v Write out the Boolean equation that maps the identified inputs to the outputs

v Draw a commensurate K-Map for the Truth Table

v Derive a simplified Boolean logic using the K-Map v Draw a schematic representation of the final and optimised circuit.

Assessment (2.2.1.AS.2). The document marks these depth-of-knowledge levels for this indicator: Level 1 Recall; Level 2 Skills of conceptual understanding; Level 4 Extended critical thinking and reasoning.

Teaching and Learning Resources:
- Real circuit board containing various
- Gates
- Breadboards
- Electronic kit
- Flip boards
- Graphs
- Online materials
- Computers with required information