/sci/ - Science & Math

[Anonymous No.4233934]

hey /sci/
Been on this problem for a while... huge mental block

How do I convert a boolean function from Sums of Products to Products of Sums form??

Example: F(A,B,C,D) = B'D+A'D+BD
In canonical form, in Sums of Products form, I get a long ass function:

F=AB'CD+AB'C'D+A'B'CD+A'B'C'D+A'BCD+A'BC'D+ABCD+ABC'D

which is F=m1+m3+m5+m7+m9+m11+m13+m15 in sum of minterms form.

How the fuck do I convert that shit into PoS form to get the Product of Maxterms form?

[Anonymous No.4233938]

bump, please I can't sleep till I solve this

[Anonymous No.4233952]

one last bump, I give up

[Anonymous No.4234003]

you're going about it the wrong way

step 1) evaluate each produt term in the SOP expression. That is, determine the bnary equivalent that represent the product terms.
step 2) determine all of the binary numbers not included in the evaluation in step 1
step 3) write the equivalent sum term for each binary number from step 2 and express in POS form

Example: A'B'C' + A'BC' + A'BC + AB'C + ABC

Solution: 000 + 010 + 011 + 101 + 111

Since there are three variables in the domain of this expression, there are a total of 2^3 possible combinations. The SOP expression contains five of these combinations, so the POS must contain the other three which are 001, 100, 110.
These are the binary values that make the sum term 0. The equivalent POS expression is
(A + B + C')(A' + B + C)(A' + B' + C)

You can verify that they are equivalent by substituting binary values into each.