All Boolean expressions, regardless of their form, can be converted into either of two standard forms:
A Boolean function can be uniquely described by its truth table, or in one of the canonical forms. A canonical form specifies a unique representation of the Boolean function, while a normal form simply specifies its form, without the requirement of uniqueness.
There are 2 steps to derive the Canonical Sum of Products Form from its truth table.
This truth table is interactive. Click on the output to change its value and observe the new Boolean Expression.
The Boolean expression of any combinational logic circuit described by a truth-table can be obtained by writing its canonical form. Use Boolean Algebra to simplify the expression which can then be translated to a circuit of logic gates.
Learn by Doing
Design an Odd Number Detector to deepen your understanding of the Sum of Products.