Boolean function - minterms - literals

[General_Sax]

Boolean function - minterms -- literals

Homework Statement

(a) Describe the circuit in a form of a Boolean function F(A, B, C, D, E). Convert this
expression to the sum of products form that includes minimal number of literals, and next
express this function as a sum of minterms, namely F(A, B, C, D, E) = m(….).

Homework Equations

xx

The Attempt at a Solution

I wrote out a truth table for the function and have a total of 11 terms. I might as well write it out here:

F = A'B'CD'E + A'B'CDE + A'BC'DE + A'BCD'E + A'BCDE + AB'C'DE + AB'CD'E + AB'CDE + ABC'DE + ABCD'E + ABCDE

next step: Convert this expression to the sum of products form that includes minimal number of literals.

Do they want me to K-map the function, or do they want me to simplify the expression algebraically (boolean algebra obviously)?EDIT: one more question: What is the difference between a complement and a dual??

 

[General_Sax]

I have another question, and I didn't want to make another thread. My question is attached into this post.

Commutative

xy = yx

Associative

x + y = y + x


so, are they asking me to prove:

(x -> y) = ( y -> x)

and

(x -> y) + (y -> x) = (y -> x) + (x -> y)


This question is really confusing me.

Thanks for help in advance.

 

[General_Sax]

Both problems solved.

Still don't understand what the difference between a compliment and a dual is though.