Final answer:
The given Boolean expression Z = CD + ABD + D(C + AB) simplifies to Z = CD + ABD by using distributive law and combining like terms. It can then be converted into Product of Sums form by expressing each term as a sum, resulting in Z = (C+D)(A+B+D).
Step-by-step explanation:
You need to convert the equation Z = CD + ABD + D(C + AB) into Product of Sums (POS) form. First, let's simplify the equation using distributive law to see if any terms can be combined:
Z = CD + ABD + DC + ABD
Notice that ABD is repeated. Now, eliminate the duplicate term:
Z = CD + ABD + DC
Now, realize that CD is a common factor of the two terms CD and DC, which can be simplified since D + D = D:
Z = CD + ABD
To convert this into POS form, we have to first express each term as a sum:
Z = (C+D)(A+B+D)
And that's the equation in Product of Sums form.