Question

Por manipulações algébricas, simplifiqye a função F dada abaixo até a forma mais simples.

 

                         _ _ _        _ _ _             _  _ _           _              _ _

F(x,y,w,z)   =   x y z   +   x y w z   +   x y w z   +   x y w   +   x y w z

Answer 1

Olá, Mineiro.

 

$<var>F(x,y,w,z) = \bar{x}\bar{y}\bar{z} + \bar{x}\bar {y}\bar{w}z + x\bar{y}\bar{w}\bar{z} + x\bar{y}w + x \bar{y}\bar{w}z=\\\\ =\bar y( \bar{x}\bar{z} + \bar {x}\bar{w}z + x\bar{w}\bar{z} + xw + x\bar{w}z)=\\\\ = \bar y[x\bar w\underbrace{(\bar z + z)}_{=1} + \bar {x}\bar{z} + \bar{x}\bar{w}z + xw]= \bar y[x \underbrace{(\bar w+w)}_{=1} + \bar{x}\bar{z} + \bar {x}\bar{w}z]=</var>$

 

$<var> =\bar y(\underbrace{x+ \bar{x}\bar{z}}_{\text{Absor\c{c}\~ao}} + \bar {x}\bar{w}z)=\bar y[x+ \underbrace{\bar{z} + (\bar{x}\bar{w})z}_{\text{Absor\c{c}\~ao}}]=\bar y[x+ \bar{z} + \bar{x}\bar{w}]=\\\\\\ =\bar y(\underbrace{x + \bar{x}\bar{w}}_{\text{Absor\c{c}\~ao}} + \bar{z})=\boxed{\bar y(x +\bar{w} + \bar{z})}</var>$