# boolean logic problem

Discussion in 'Homework Help' started by fran1942, Apr 7, 2013.

1. ### fran1942 Thread Starter Member

Jul 26, 2010
58
0
Hello, I had to do complete the problems as outlined below this paragraph. I completed parts a-b as per the attached image, however I cannot complete part c which is 'how to use De Morgan's theorem to prove a relationship between the two Karnaugh map simplified formulas'. Can anyone see what I am doing wrong here ?
Thanks kindly for any help.

(a)
Design a circuit which has the four bits of a BCD number as its inputs and
has an output X so that:
X = 0 if inputs are a valid BCD number
X = 1 if inputs are an invalid BCD number.
(b)
Redesign the circuit of (a) so that:
X = 1 for valid BCD
X = 0 for invalid BCD.
(Note: DO NOT just invert your input (a).)
(c)
Use de Morgan’s theorem to prove that the Boolean Algebra expressions
you obtained in (a) and (b) are the inverse of each other.

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2. ### WBahn Moderator

Mar 31, 2012
24,553
7,691
How can we tell what you are doing wrong on Part C when you haven't shown us what you are doing on Part C at all?

Your Part A and Part B work is fine.

Post your best effort for Part C so that we have a springboard to work from.

3. ### djsfantasi AAC Fanatic!

Apr 11, 2010
5,434
2,056
Hint!

Rewrite your solutions in parts a and b, to use different variables:

X=A(B+C)
Y=A'+B'C'

Then, to prove part C, you need to show that X and Y' are the same. Using DeMorgan's, this is easy...