Willing to pay a good amount of forum gold for someone to help me out. I am stuck I cant figure out how it really works, I understand the basic rules of it but I don't think I am getting the right answers what so ever. Also, I cannot use K-Maps on this has to be done out.

For example I have

D'C'B'A+D'C'BA'+D'C'BA+D'CBA'+D'CBA+DC'B'A'+DC'B'A+DC'BA'+DC'BA+DCB'A'

and I simplified it to C' which i have a big feeling that its not right at all.

Not looking for someone to do my homework for me, looking for someone to help me get a better understanding on the subject and help me be able to achieve the correct answer on my own. Willing to pay well for help with this.

have you tried drawing a truth table? see which ones are valid, which are not valid, then factor out

http://sandbox.mc.edu/~bennet/cs110/boolalg/rules.html

/edit: personally i prefer sum of products. i forgot, what does simplified mean? fewest transistors? fewest terms?

This post was edited by carteblanche on Sep 17 2013 07:23pm

trying to get the least amount of terms possible to equal the original equation

how exactly did you get to C'? that definitely looks wrong considering that there are several terms where C is allowed to be true

by cancelling out the ' with the non ' and it ended up there..

This post was edited by Acdc-rocks[tom] on Sep 17 2013 07:52pm

show your steps one by one. it's possible you know how to do it fine but you're confused with the equivalence laws or just made a mistake

This post was edited by carteblanche on Sep 17 2013 08:06pm

D'C'B'A+D'C'BA'+D'C'BA+D'CBA'+D'CBA+DC'B'A'+DC'B'A+DC'BA'+DC'BA+DCB'A'

D'CBA+DC'B'A' = i think this term cancels

DC'B'A + D'CBA' = think this cancels also

D'C'B'A + DC'BA' = C'

DC'BA+DCB'A' = D

DC'BA' + D'C'BA = C'B

D'C'BA' + C' + D + C'B = C' + B ( forgot the B in my answer previously )

but thats what I did and i think im missing something..

wait, what do you mean "this term cancels"? i think that's your problem.

lets look at a simple example.

f(a, b ) = ab' + a'b

i assume you want to cancel that out? that's the expression for exclusive or (XOR). either a is true or b is true, but not both. you can't simply cancel them out and put T or F for all inputs of a and b. clearly, f(T, F) = T and f(F, T) = T, but f(T, T) is false and f(F, F) is false.

you can reduce something like say, f(a) = a + a' since it returns true regardless of input.

i think you should go back to truth tables and play around with them. though i guess that's essentially what the kmap does.

This post was edited by carteblanche on Sep 17 2013 08:19pm

so what would that just turn to (a+b)'?

(a+b)' = a'b' is de morgan's theorem. looks like your problem is that you dont really understand what's going on. you need to focus on that before you worry about simplifying imo. look over the laws and practice them with truth tables.

/edit: looks like de morgan's theorem is what you're missing conceptually. you think (abcd)' = a'b'c'd' which is NOT the case. you have to invert everything inside and also switch the operator. conceptually this should make sense.

if any of the things inside is false, then the whole expression (abcd) becomes false. so when you complement it, it becomes true. so to make (abcd)' become true, any of the variables must be false. whereas a'b'c'd' means that everything must be false, as opposed to any. so (abcd)' = a' + b' + c' + d'

keep in mind that when OR'ing terms (or summing them), if any term is true, then the whole expression is true. which is why i like sum of products personally. it's very clear to see what inputs make the whole thing true.

This post was edited by carteblanche on Sep 17 2013 08:32pm