Lecture 7: Min Terms and Max Terms

Overview

• Discussion focuses on concepts from Units 3 and 4.
• Main focus: Understanding Min Terms and Max Terms in Boolean functions.

Min Terms

• Definition: A min term is the product of all Boolean variables in either complemented or uncomplemented form.
• Example: For Boolean function f(X, Y, Z):
  • Terms like X'Y'Z and XY'Z' are min terms.
  • Terms like X'Y, YZ, or X are not min terms.

Identifying Min Terms

• A min term involves all available Boolean variables.
• Example:
  • G(X, Y) = XY' is a min term if only X and Y are considered.
  • Context matters: need to know all Boolean variables in the problem.

Truth Tables and Min Terms

• Min terms yield a value of 1 under only one configuration of variables.
• Truth table analysis helps identify which configurations result in a '1'.

Minterm Expansion

• Purpose: Express a function in terms of its min terms.
• Each min term corresponds to a truth table row where the function evaluates to 1.
• Notation: f(X, Y, Z) = Σm(1, 2, 5) where numbers indicate min terms.

Examples

• Example 1: f(X, Y, Z) with a truth table shows which min terms contribute to '1' values.
• Example 2: Creating a truth table for G(X, Y, Z) using its min terms.

Conversion to Minterm Expansion

• Can convert complex expressions to minterm expansion:
  • Use identities: 1 = X + X' to fill in missing variables.
  • Simplify using distributive properties.

Max Terms

• Not yet discussed in detail; upcoming in next lecture.

Practice Problems

• Problem 1: Identify valid expressions representing a given truth table.
• Problem 2: Find the minterm expansion for a function G(X, Y, Z).

Conclusion

• Understanding min terms is crucial for simplifying and analyzing Boolean functions.
• Next lecture will cover Max Terms and their applications.