problem with some gate

roeyhaim

Joined Nov 22, 2010
6
hello guys.
I'm stuck with a problem and need help...

This is the Q:
Introducing new operator ("smile")
with the following logic: A B = A'B
Express function F(x,y,z) =∑(4,6,7) using only operator and construct a circuit diagram for this function using ONLY "smile" gate.
I tried for all night and didn't get it....
any suggestion?

thatoneguy

Joined Feb 19, 2009
6,349
Where are you stuck?

$A\smile B= A\overline{B}$

Apply that to the function, have you had previous examples of applying logic to a function?

roeyhaim

Joined Nov 22, 2010
6
well i tried to simplify the function.
I got F(x,y,z) = xy + xz'

but i dont know how to continue...

thatoneguy

Joined Feb 19, 2009
6,349
Here is a similar example Without the Georacer

Joined Nov 25, 2009
5,154
You did well simplifying the function. Your task from now on is to convert any single operation to a smile operation. Start with a factorization.

Here are some hints:
a+b'=(a'b)'
x'=(x'1)

Can you figure it out?

renotenz

Joined Oct 25, 2010
11
well i tried to simplify the function.
I got F(x,y,z) = xy + xz'

but i dont know how to continue...
You can still simplify that function actually... there's one common letter there

After that you shall see a pattern which Georacer already wrote.

Also remember that : A'B = BA'

Cheers <= Smile function for you roeyhaim

Joined Nov 22, 2010
6
I'm sorry, but i still don't get it...

I give up...

My brain is gonna explode.

Thanks for trying Now I scared from the yellow smile Georacer

Joined Nov 25, 2009
5,154
Don't give up yet. Try a bit more. You have problems doing the factorization? Finding the part to be substituted?

Post any scribbles you have done, even if they are completely wrong. Don't let a good thread end without a closure.

roeyhaim

Joined Nov 22, 2010
6
OK...
but please dont laugh at me...

i thought maybe to put the x out and then to play a little with the y

maybe to do some demorgan.

but the Q is what to do with the +

any hint / advise?

renotenz

Joined Oct 25, 2010
11
There it is.

Put X out, then you'll get X(Y + Z')

See any resembelance with what Georacer has typed?

Don't forget that your is A'B, same as BA', same as X'Y, YX', etc...

roeyhaim

Joined Nov 22, 2010
6
so, tell me if im right

now i got X(y'z)'

and put this in circuit :

X 1 = X'
Y Z = Y'Z
Y'Z 1 = (Y'Z)'
X' Y'Z = X''(Y'Z)'

X''(Y'Z)' = X(Y+Z')

Am I right?
This is the solution?

Georacer

Joined Nov 25, 2009
5,154
Not quite.
Y'Z 1 = (Y'Z)' is correct only with parentheses: (Y'Z) 1 = (Y'Z)' and
X' Y'Z = X''(Y'Z)' is wrong.
You have also written down some unneded equations. So let's sum it up:

xy+xz'=
x(y+z')=
x(y'z)'=
(y'z)'x=
...

Can you take it from here and substitute for the operation? Make one step at a time and start from inside out.

thatoneguy

Joined Feb 19, 2009
6,349
From the original question, the solution should have the operator only, so go through the steps to substitute it, and leave it (and ONLY the ) in for the final solution.

roeyhaim

Joined Nov 22, 2010
6
sorry but im lust again...
I feel so What i need is to figure out how to get
X(Y'Z)' by input to a gate only two variables?

with no other gates?
just ONE AND ONLY gate?

thatoneguy

Joined Feb 19, 2009
6,349
As I read it, you can use all the gates you want, but you aren't allowed to have an inverter.