Part 3: Sum of Products (SOP) Find the sum of products for the following expressions. Show your result in the algebraic form AND the summation form. Show all steps for each process and put a circle or box around your final answer. a) F = (b + cd)(c + bd) b) F = (bd + cd)(c' + bc) c) F = (bc + d')(c + b'd) d) F = (b'c + c'd) (bd + cd)
a) F = (b + cd) (c + bd)
Expanding the expression using the distributive law:
F = b(c + bd) + cd(c + bd)
F = bc + bbd + ccd + bcd^2
Using the fact that bbd and bcd^2 are redundant terms:
F = bc + ccd + bcd
The sum of products in algebraic form is:
F = bc + ccd + bcd
The sum of products in summation form is:
F = Σm(1, 3, 5)
where m stands for the minterms that are included in the sum of products.
b) F = (bd + cd)(c' + bc)
Expanding the expression using the distributive law:
F = bdc' + bbc' + bdd + cdc' + cbc'
Using the fact that bbc' and cbc' are redundant terms:
F = bdc' + bdd + cdc'
The sum of products in algebraic form is:
F = bdc' + bdd + cdc'
The sum of products in summation form is:
F = Σm(2, 3, 6)
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