Digital Electronics Lecture Notes: Six Variable K-map

Overview

• Instructor: Professor Dholakia
• Topic: Solving a six-variable K-map using Boolean expressions.
• Format: Problem-solving session.

Key Concepts

• Karnaugh Map (K-map): A tool for simplifying Boolean expressions.
  • Variables: In this session, we focus on six variables (n = 6).
  • Total Cells: 2^n = 2^6 = 64 cells in the K-map.

Structure of K-map

• The K-map is divided into 16 groups of 4 cells each.
• Variables: Grouped as A, B and C, D, E, F.
  • A, B can be either 0 or 1.
  • C, D, E, F structure follows the 16-cell K-map configuration.

K-map Layout

1. Group A, B: 0 0, 0 1, 1 0, 1 1
2. Group C, D, E, F: 00, 01, 11, 10 (for each combination)
3. Addressing Cells: Location assignment from 0 to 63 based on the binary combinations:
   • Example: A, B = 00 maps to the first row of the K-map.

Identifying Locations of Ones

• Locations of 1s: 0, 5, 7, 8, 9, 12, 13, 23, 24, 25, 28, 29, 37, 40, 42, 44, 46, 55, 56, 57, 60, 61.

Grouping Ones

1. First Group: Combine cells to form the largest group possible.
   • Example: Combine two groups of four to form an 8-cell group.
   • Common Variables: Identify common variables in each group.
2. Subsequent Groups: Continue grouping while maximizing the size of each group.
3. Final Groups: Aim to cover all 1s in the K-map with minimal groups.

Groups Formation Summary

• Group 1: BC E'
• Group 2: A' C D'
• Group 3: A' B' C F'
• Group 4: C' D E F
• Group 5: B' C' D E F
• Group 6: A' B' C' D F'
• Group 7: A' B' D' E' F'

Conclusion

• Final Boolean Expression: Combine all groups to form the final Boolean expression.
• Practice Recommended: Follow the explained steps for better understanding and efficiency.

Feedback Request

• Professor encourages students to provide feedback on the session to improve teaching methods.