# Venn Diagrams and Boolean Algebra

A *Venn diagram* may be used to represent the possible logical states of a combinational logic system, typically having up to 3 input variables.

Venn diagrams with more than 3 input variables becoming increasingly difficult to draw, given that forNvariables, there must be 2^{N}unique regions

Each enclosed region of a Venn diagram represents a single line of the equivalent truth table, which is also known as a *minterm*. Areas of the Venn diagram are shaded if the corresponding minterm is equal to one.

The following illustration gives examples of some simple logic functions represented in Venn diagram form.

While Venn diagrams are a useful tool for visualising combinational logic functions, they are not used for logic simplification. The closely related Karnaugh map is preferred for this purpose.

#### Problem 1

State the equivalent logic functions for the following Venn diagrams.

- NOT B
- NOR
- AND (3 variable)