Let us revisit equation 1. Can we do better than this? Can we simplify the equation, somehow?
A quick visual inspection reveals that we have both the terms XY Z′ and XY Z in the sum. XY Z′ + XY Z = XY (Z′ + Z) = XY (1) = XY . In other words, we can optimize Z out of the equation, yielding W = X′Y ′Z′ + X′Y Z + XY ′Z′ + XY . Next, we recognize that we have X′Y ′Z′ + XY ′Z′ = Y ′Z′. This further reduces the equation to W = Y ′Z′ + X′Y Z + XY .
Can we reduce the equation any further? Is there a systematic method to simply Boolean functions?