Product of sum to sum of product

Question

(A+B+C+D’)(B+C’+D)(A +C)(A+C)

This is the expression that I have to convert to sum of product.

I got (A'B'C'D)+(B'CD')+(A'C')+(A'C')

I'm not really sure if I'm right... If I am, can I combine the (A'C') and write as 2(A'C')??

Please help

Answer 1

Here the + refers to ORing and . refers to ANDing operations. (A'C')+(A'C') means that A's complement is ANDed with C's complement which is ORed with the ANDing of A's complement with C's complement.

Answer 2

As Ashis says, (A'C')+(A'C') is just (A'C').

To simplify your expression, use a Karnaugh map (see http://en.wikipedia.org/wiki/Karnaugh_map).

To check your answer, compare its truth table with the original expression. For example, in Maxima,

(%i1) load(logic)$
(%i2) orig : (A or B or C or (not D)) and 
       (B or (not C) or D) and 
       (A or C)  and (A or C)$
(%i3) your_answer: ((not A) and (not B) and (not C ) and D) or
       ((not B) and C and (not D)) or
       ((not A) and (not C)) or
       ((not A) and (not C))$
(%i4) logic_equiv(orig,your_answer);
(%o4) false
(%i5) characteristic_vector(orig);
(%o5) [false,false,false,true,false,false,true,true,true,true,false,true,true
        ,true,true,true]
(%i6) characteristic_vector(your_answer);
(%o6) [true,true,true,false,true,true,false,false,false,false,true,false,
        false,false,false,false]

or, for just one case,

(%i7) orig, A=true, B=true, C=true, D=true;
(%o7) true
(%i8) your_answer, A=true, B=true, C=true, D=true;
(%o8) false