# Transform function to bases

Discussion in 'Homework Help' started by danya, Oct 29, 2013.

1. ### danya Thread Starter New Member

Oct 29, 2013
2
0
I have a function (A xor C) nand (B xor c)
In other form it's: $(AC) + (\neg AB) + (\neg B\neg C)$

The task is to transform the function to bases
1. NOR
2. NAND
3. EQV, COIMP ($\neg \rightarrow)$
4. XOR, IMP
5. NOT, AND

Tried using De Morgan's but I'm always getting unwanted 1, 0 or $\neg$, do you have any ideas?
Thanks!

Last edited: Oct 29, 2013
2. ### WBahn Moderator

Mar 31, 2012
18,093
4,920
I think I have an idea, but what exactly do you mean by "transform the function to bases"? Specifically, what do you mean by "bases"?

Something that is not seen very often is implication and what I assume you are calling converse implication. So we should be sure we are meaning the same thing, especially since they are not symmetric.

Are these the truth tables you intend for these two functions:

 A B A $\neg$ B A $\neg \rightarrow$ B F F T T F T T F T F F T T T T T

Next, you need to show us YOUR efforts to solve YOUR homework problem. They don't have to be right, but then need to be there so that we have a starting point for discussion.

3. ### danya Thread Starter New Member

Oct 29, 2013
2
0
Transforming the function to base is representing the function using only those operations that are included in base. By co-imp I assume the negation of implication.

A B Impl Co-imp
F F T F
F T T F
T F F T
T T T F

I've tried to transform the function using identities like:
A nand A = $\neg A$
A nor A = $\neg A$
(A nor A) nor (B nor B) = A$\wedge$B
and De Morgan's Law but function had become very huge and unreadable.

4. ### WBahn Moderator

Mar 31, 2012
18,093
4,920
You might want to verify your assumption. You may be right and that what your instructor/author means is "complement of implication" instead of "converse implication". But these two are different. For negation of implication, I prefer to use the same convention that we use for negation of AND (i.e., NAND) and negation of OR (i.e., NOR). Thus, what you describe in your truth table I would call NIMP.

I would recommend doing the truth table for the function you are trying to implement and then figuring out what gates are needed for each base from there. If the requirement is to show the development using Boolean algebra, then knowing the solution you are headed toward will often give you the clues for what path to take to get there.