Find the complement of the following expression and simplify: `x bar y + y bar z`Sorry i dont know how to do the not sign above the Z and y :/ .
The complement of the above Boolean expression is:
To simplify, use De Morgan's Theorem which is `bar(A+B)=barA*barB` .
Again, use De Morgan's Theorem to simplify further. The formula is `bar(AB)= barA+barB` .
> `= (barx+ bar(bary))*(bary + bar(barz))`
Note that `NOT(barA)=A` .
> `= (barx+y)*(bary+z)`
> `=barxbary + barxz + ybary + yz`
Apply the law of Boolean algebra which is `AbarA=0` .
> `= barxbary+barxz+yz`
Hence, the complement of `xbary+ybarz` is `barxbary+barxz+yz` .