Boolean algebra #25: DeMorgan's theorem - examples (continued)

[MrAloke7]

what is word in computer terminology ?

[MrAloke7]

can u tell me that which operation perform first in the boolean expression A + ( B.C ) { there is a bar above B.C ] ? the option i got in the question are a ) AND b ) OR c ) NOT d ) All of them .

[keleshevCOM]

@mwoddo, @00Gravity,

There are two ways of simplifying (C' + (CD)')' [mind that it's (CD)' and not C'D'].

First way to apply DeMorgans for the whole expression first:

(C' + (CD)')' = C'' * (CD)'' = CCD = CD [as I did in the video],

The other way is to apply DeMorgans on (CD)' first [as you, guys, propose]:

(C' + (CD)')' = (C' + C' + D')' = CCD = CD

In both case the result is the same.

[mwoddo]

@keleshevCOM please tell us if why it is not c+d

[00Gravity]

hello, by (A´+B)(B´+(C´+C´D´)´), why does (C´D´) not become C+D? Is that because of the doble negation whereas by (AB´)´ there´s only one negation of the sign in between? Thank you very much!

[Morelloo1]

I like the video it is very helpful. But I have a question. If we are given a function F = ABC' + BC + C'D (where the ' after the letter is bar) and we need to express the function with only OR and compliment operation and then again with only AND and compliment operation how do we figure out the OR and compliment operation because isn't the original equation already in sum of products form?

[keleshevCOM]

@Morelloo1 To represent your function with only use of complement (negation) and OR (+ sign) but without AND (multiplication sign) I would double-negated every term and applied DeMorgan's theorem to them:

ABC' + BC + C'D =

(negate twice every term)

((ABC')')' + ((BC)')' + ((C'D)')' =

(applying DeMorgans thorem)

(A' + B' + C)' + (B' + C')' + (C +D')'

no multiplication in this one!

Hope I explained ok.