Engineering Simplifying switching circuit literals

[toforfiltum]

Homework Statement

The problem is given in the picture attached. It is a network of switches.

Homework Equations

The Attempt at a Solution

I managed to simplify the expression to this:

$(S + x'(w+y) + xvz)(x'+y)(v+z')$

but I just can't find a way to simplify it to 9 literals. I've tried all different methods I can think of, but I just can't find the trick.

The last method I came up with(that I thought was pretty close) was this:
$S(x'+y)(v+z')+(xvzy+x'y(v+z')+xvzy)$

I tried to multiply out the expressions to the right of $S$, hoping that I could eliminate the duplicate literals. I thought that by adding the extra literal $xvzy$ I could eliminate more literals, but this approach didn't work. I'm really stuck. I have been trying this for hours. Any ideas?

Thanks!

 

[NascentOxygen]

$(S+x′(w+y)+xvz)(x′+y)(v+z)$

Can you explain how to count the literals in this expression?

 

[toforfiltum]

Can you explain how to count the literals in this expression?

I would count the number of terms in a SOP form. Would that be right? So I think I may be wrong, 9 circuit elements means just 9 switches?

 

[NascentOxygen]

Where does the goal of fewer than 9 come from? Are you given the answer?

I count 7 literals in your expression I quoted.

 

[toforfiltum]

I'm sorry, although I now understand the distinction, I still can't get the right answer

Where does the goal of fewer than 9 come from? Are you given the answer?

I count 7 literals in your expression I quoted.

I'm not too sure if I know what the question asks, but it states that the final form needs to be simplified to 9 switching elements. And no, I don't have the answer.

Does a switching element correspond to a single switch? If so, I must simplify it to 9 switches.

 

[NascentOxygen]

Nine switches sounds a reasonable goal. Before you spend many hours trying to simplify to 9, it might be worth demonstrating that $(S+x′(w+y)+xvz)(x′+y)(v+z)$ does still correctly correspond to your original figure, perhaps test both for a couple of sets of arbitrary inputs. It would be easy to have an error creep in.