In all of these equations, are (x_a) and (x_b) Boolean values (i.e., either a 0 or a 1)?

So I can simply take out (x_a) and (x_b) right? and the answers to the four senarios would be:
When (x_a) is to Vref and (x_b) to ground: Vut = (3/4)*Vref

When (x_a) is to ground and (x_b) to Vref: Vut = (1/2)*Vref

When both (x_a) and (x_b) are to Vref: Vut = (3/4)*Vref

When both (x_a) and (x_b) are to ground: Vut=0

Or are my calculations wrong?

 

You are close. Ask if all of your answers make sense. In particular, if both switches are to Vref you say that the output is (3/4)*Vref. Now you switch (x_b) to ground and you are saying that doing so has no effect on the output. Does that make sense?

 

You are close. Ask if all of your answers make sense. In particular, if both switches are to Vref you say that the output is (3/4)*Vref. Now you switch (x_b) to ground and you are saying that doing so has no effect on the output. Does that make sense?

Ohh yeah I did a mistake when (x_b) is to ground and (x_a) is to Vref.
It should go Vut = Vref-6*I2*R=2*I2*R

so Vut = (1/4)Vref
right?

 

That's what I expect -- I haven't actually cranked the math.

Have you learned superposition yet?

 

That's what I expect -- I haven't actually cranked the math.

Have you learned superposition yet?

No I haven't, but I read about it briefly now and I can see how you caught my error

 

No I haven't, but I read about it briefly now and I can see how you caught my error

I didn't use superposition. I caught your error exactly as I described it -- by asking if the answers make sense.

Two rules that, if followed religiously, will help you catch the overwhelming fraction of your mistakes:

1) Always, always, ALWAYS track your units.
2) Always, always, ALWAYS ask if the answer makes sense.

The reason that I mentioned superposition is that problems like this really lend themselves to it. Plus, not only do you get an answer much quicker, but you can build up the general case answer very easily so that if someone tells you the switch positions you can almost immediately tell then the output voltage.

 

I didn't use superposition. I caught your error exactly as I described it -- by asking if the answers make sense.

Two rules that, if followed religiously, will help you catch the overwhelming fraction of your mistakes:

1) Always, always, ALWAYS track your units.
2) Always, always, ALWAYS ask if the answer makes sense.

The reason that I mentioned superposition is that problems like this really lend themselves to it. Plus, not only do you get an answer much quicker, but you can build up the general case answer very easily so that if someone tells you the switch positions you can almost immediately tell then the output voltage.

Thank you I will keep that in mind.
Thank you so much for your help and patience!!