Example of an SOP:

Y $($A$,$B$,$C$)=$m$(0,3,5,6,7)=$ A$$B$$C$+$ A$$BC $+$ AB$$C $+$ ABC$+$ ABC

Another way to implement logic functions is to use a Product of Sums $($POS$).$ Truth table zero outputs are considered in this form. The variables corresponding to a zero are negated and OR$$ed into a maxterm. These combinations are then AND$$ed with each other.

Example of a POS:

Y$($A$,$B$,$C$)=\backslash$Pi M$(0,1,5,6)=($A $+$ B $+$ C$)($A $+$ B $+$ C$)($A$+$ B $+$ C$)($ A$+$ B$+$ C$)$

A Boolean expression can be simplified using Boolean algebra and$/$or a Karnaugh Map $($K$-$Map$).$ The K$-$Map groups elements with common functions in a table$-$like form. The data in a truth table $$maps$$ into the K$-$map so that they both contain the same information.