CODEWITHSUNDEEP
booleanboolean-logicboolean-expression
user10443894
user10443894

Reputation:

How to simply (AB')' or (ABC')'?

Stuck on one aspect of a question for Computer Architecture I: Digital Design, and am not sure how to simplify (ABC')' or even (AB').

Not sure if any axiom or theorem can be applied, or if (ABC')' [or (AB')'] is the most simplified form. Can someone confirm?

Upvotes: 0

Views: 212

Answers (2)

Patrick87
Patrick87

Reputation: 28312

To expand upon what Amadan said:

(AB')' + (ABC')'
A' + B + A' + B' + C          DeMorgan applie twice
A' + A' + B + B'+ C           commutativity of disjunction
A' + B + B' + C               x + x = x
A' + 1 + C                    x + x' = 1
1 + C                         x + 1 = 1
1                             1 + x = 1

Upon reflection this must be the case since B must be either true or false, and each of these values makes one or the other of the original terms true.

Upvotes: 0

Amadan
Amadan

Reputation: 198456

You can splat (ABC')' into A' + B' + C; similarly, (AB')' is A' + B (according to De Morgan's laws). These are disjunctive normal form.

Upvotes: 0

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