Combinational Logical Circuits

Representation

Karnaugh Map

A diagram which can be used to reduce a truth table of inputs and output to a boolean expression.

• Sketch an empty with (1 vs 1 or 1 vs 2, or 2 vs 2 …)
  • If the variables in a row or column is more than 2, they must be arranged in gray code.
• Populate the map with given values
• Group the 1s according to K-map rules

Then the boolean expression can be derived.

Sum of Products

• Pick all the 1s
• Construct literals using the inputs, AND operator, so that they result in a 1.
• Sum all those operators

Minterm

A product of literals.

Product of Sums

• Pick all the 0s
• Construct literals using the inputs, OR operator, so that they result in a 0.
• Join all those literals using AND operator

Maxterm

A sum of literals.