ECE 2020 Digital Design

Prof. Matthieu Bloch

Monday, September 8, 2025 (v1.0) - Karnaugh maps

Last time

  • Last time
    • We started talking about Karnaugh maps (or K-maps)
    • K-maps will allows us to convert truth tables into simplified boolean expressions
  • To be effectively prepared for today you should have:
    • Read textbook Sections 1.2, 1.4, 3.0-3.1
    • Read your notes and reviewed the examples
  • Important notes
    • Homework 2 due Monday September 15, 2025
    • Breanna's office hours Thursdays 2-3pm in TSRB 530
    • Dr. Bloch's traveling on Wednesday September 10, 2025
      • Recitation with Mr Yun-Feng Lo
      • Asynchronous lecture
  • Today
    • We will finish Karnaugh maps
  • Be ready!
    • You will be asked to doodle a few things on a writing support
    • We will take a quizz on canvas to see if my attendance taking system works

Homework 1 debrief

  • Thanks for your feedback (26 respondents + Breanna's input)
    • 50% found the homework moderate, 47% challenging
    • 78% were somewhat prepared, 11% not prepared
    • 67% spend 3-6 hours, 28% 6-9 hours
    • 81% did not use AI tools
  • Office hours and tutoring can help greatly
    • Consider attending
    • Plan a bit

Karnaugh maps

  • We are first introducing K-maps as a recipe
    1. Draw the truth table on a grid
      • Use Gray mapping to ensure only one bit changes at a time across rows and columns
    2. Identify implicants
      • Group in buckets of size \(2^i\) for \(i\in\mathbb{N}\) as large as possible
      • Only extend vertically and horizontally
      • Identify essential and non-essential prime implicants
    3. Compute formula from implicants

Example 1

  • \(F(A,B,C) = \Sigma m(0,1,4,5)\)

Example 2

  • \(F(A,B,C) = \Sigma m(0,1,4,6,7)\)

Example 3

  • \(F(X,Y,Y,Z) = \Sigma m(0,1,2,3,5,7,9,10,11,13)\)

Until next time

  • To be effectively prepared for Wednesday September 10, 2025, you should:
    • Chapter 3
    • Read your notes and review the examples
  • Coming up
    • Recitation on Wednesday September 10, 2025
    • Asynchronous lecture - please watch by Monday September 15, 2025
    • Homework 2 due on Monday September 15, 2025
    • First test in class on Wednesday September 17, 2025