Objectives

Students will be able to:

  • develop a Karnaugh Map for a given truth table.
  • use the Karnaugh Map to create a simplified logic statement for a circuit.

Karnaugh Maps

1. Intro to Karnaugh Maps

One goal of circuit design is to make the logic in the circuit as efficient as possible and reduce or eliminate any redundant logic.

A popular method to achieve this goal is the use of Karnaugh Maps.

With a little practice this becomes a very straightforward process.

EE Prof Lady has created a really clear video on how to produce a K-Map and then use it to simplify a circuit's logic.

Observations

For a 3-input circuit:

  • Break the map into an A section and a BC section
  • Note that the 4 combinations in the BC section can only differ by 1 bit, hence the 00, 01, 11 10 sequence
  • Note that the logic statement often uses ' to denote NOT eg B' is the same as NOT B
  • Use OR logic to piece together the final logic statement.

Challenges

Complete the three challenges presented in the worksheet.

2. More Karnaugh Maps

What if we start with a logic statement instead of a truth table?

eg

output is 1 if (A'B'C) + (AB'C) + (ABC)

Let's take a look at how to deal with this situation.

Challenges

Complete K-Maps for these 3 logic statements.

output is 1 if (A'BC)+(A'BC)+(AB'C')+(ABC')

output is 1 if (A'B'C)+(A'BC')+(ABC')+(ABC)

output is 1 if (A'B'C)+(A'BC')+(AB'C)+(ABC)