boolean algebra problem(sum of minterms)

[Dr deo]

Hi,
Am having trouble with boolean algebra. The problem is with with converting an expression to its standard form( canonical form) as a sum of minterms . The function F=C + AB, is shown in two forms.
As a sum of minterms on the left and converted into optimal form on the right. But how does the C + ABC'
turn into C +AB. (Where did the C') disappear to?

ABC + A' B C + A B' C + A' B' C + A B C' = BC (A+A') + B'C (A+A') + ABC'

                                                         =B C + B 'C + A B C'                  //     A+A'=1

                                                         =C (B + B') + A B C'                 //      B+B'=1

                                                         =C + A B C'

                                                         =C + AB

[vtheron]

oops, that wasn't quite right. Here's the correction:

C + ABC'

= ( C' (A'+B'+C) )' // DeMorgan's theorem
= ( A'C' + B'C' + CC' )'
= ( A'C' + B'C' )' // CC' == 0
= ( C'(A'+B') )'
= C + AB // DeMorgan's again

-Theron

[cpns]

... and this has what to do with C, C++, Dev-C++ or Bloodshed!? There are no doubt more appropriate forums for this.

Are you sure that this is correct? I am a bit rusty perhaps, and may be misinterpreting the notation, but doesn't C + A B C' reduce ot just C?

I am going to come back to this if I may, when I have had breakfast and found some juice for this laptop!

Clifford

[vtheron]

Use DeMorgans theorem twice:

C + ABC' = C' (A'+B'+C) // DeMorgan's theorem
= A'C' + B'C' + CC'
= A'C' + B'C' // CC' == 0
= C'(A'+B')
= C + AB // DeMorgan's again

Peace,

-Theron