Basically I have this:

F(w, x, y, z) = wx’ + y’z’ + w’yz’

and I need to Implement the following function with two level NOR gate circuit. The hint given was to use k-map.

I kinda know what the two level NOR gate circuit is but not too sure and I don't know why we need to use k-map here.

 

If you can solve the problem without using a k-map then go for it.
If not, then you kinda need to learn how to generate one.

 

I just dont really know how the two level NOR gate circuit is suppose to look like. I tried searching on google but theres so many different pictures, can't tell which one is which.

Thanks

 

It just means that you have a set of NOR gates that your inputs feed into and then the outputs of these feed into another NOR gate from which your final output is taken.

 

so it will be in this case, three NOR gates which inputs into one NOR gate?

 

so it will be in this case, three NOR gates which inputs into one NOR gate?

Why do you say that?

It would really help if you provided a sketch of what you have in mind, because I don't think you are looking at things correctly (but I could be wrong).

 

something like this??

 

That's the topology you are looking for. But why did you put three gates in the first layer? I still suspect you are not looking at it correctly. I won't be able to tell until you assign signals to the inputs.

 

It was just a drawing , in my question I guess there will be only two inputs for the first one. Correct? which will be w and x'

 

It was just a drawing , in my question I guess there will be only two inputs for the first one. Correct? which will be w and x'

And now you've confirmed that you aren't thinking about the problem correctly.

Oh, and your drawing IS wrong, because you are showing OR gates, not NOR gates. Huge difference.

 

How would we make it into NOR gates, if it possible you can should me a diagram?

 

nvm I found out you had to draw that little circle infront of the or gate to make it nor.

But since its in S.O.P I have to change it to P.O.S and then I put the inputs?

 

nvm I found out you had to draw that little circle infront of the or gate to make it nor.

But since its in S.O.P I have to change it to P.O.S and then I put the inputs?

You put the circle at the OUTPUT of the gate. An OR gate with circles at the inputs is a NAND gate.

And, yes, you have to put it in P.O.S. because, if you apply DeMorgan's Theorem to a two-level NOR topology you will find that it is functionally identical to a first layer of OR gates followed by a single AND gate, which implements a product of sums.

If you use NAND gates instead of NOR gates and again apply DeMorgan's you will discover that that topology is functionally equivalent to a first layer of AND gates followed by a single OR gate, which implements a sum of products.

You can certainly start with the SOP form and bang away at it to get it into POS, but a much simpler way is to build a Karnaugh map for F from the SOP equation and then invert everything to get the K-map for F'. Then get the SOP for F' and invert that, using DeMorgan's, and you will have the POS for F.

 

So it would look something like this? Like the NOR gate diagram?

 

View attachment 92622 So it would look something like this? Like the NOR gate diagram?

Look at it!

Now you have a layer of NOR gates followed by an OR gate. Does that really qualify as two levels of NOR gates.

You REALLY need to work on your attention to detail -- you will have nothing but problems until you do.