Hi everyone,
I was looking back in my old math notes and found the definition of IMPLIES:
xIMPLy=(NOTx) OR y.
The way I remember the table for IMPL is:
"The True (1) cannot IMPLY something False (0)".
On the other hand, I am not sure about the exact meaning of question 1 in the 2nd assignment: does it mean we have to show that every column has to be written as a combination of AND and NOT or OR and NOT?
Or it means that we have to show that every bynary function (column in the table) can be written using at least one of the operators AND, OR, NOT? Am I trying to simplify things now, or this is what is being asked?
Thanks,
Ella
3 comments:
Question one I am asking you to show that each column of the table can be written as a composition of the inputs, x & y, and the operations AND, OR, and NOT.
For instance xIMPLy can be written as NOTx or y. This answer is not unique, but it there are 'minimal' ways of doing this. It is hard to find the minimal expression in terms of AND, OR and NOT.
You don't *have* to use AND, OR and NOT. For instance the columns x, and y you don't really need them.
-Mike
HI Ella,
I also looked back on my notes and found that the truth table for xIMPy is T=>T = T, F=>T = T, F=>F = T, T=>F = F.
As for question 1, I believe you can use combos of AND, NOT, OR such as {and}, {not}, {or}, {and, not}, {or, not}, and so on...
For example, to get NAND=(1110) using x=(0011) and y=(0101), you can write NOT(xANDy).
Similarly, I believe you could just use NOT to get NOTy=(1010) by simply applying NOT to y=(0101).
Hope this is right.
Paul
Thank you Mike and Paul for your comments.
I was thinking about the meaning of question 1 because it seems that we seriously are into logic. To prove that something can be written using
("and" or "or") and "not"
means it can be written either ("and" and "not") or
("or" and "not").
Now, from your comments I understand that I made it too complicated and we are asked to prove that all 16 functions can be written using at least one of x, y, AND, OR, NOT.
Thank you again!
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