Help with Gates and Circuits Please!

Discussion in 'Homework Help' started by scubagabriella, Sep 22, 2013.

  1. scubagabriella

    Thread Starter New Member

    Sep 22, 2013
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    Simplify the following expression and implement the circuit with the minimum possible gates.

    I can make the truth table but I cant figure out the diagram part, can someone please help me?

    The ' means its a 0.

    X=AB+AC'+A'C
     
  2. WBahn

    Moderator

    Mar 31, 2012
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    You need to show YOUR best attempt to solve YOUR homework problem. That will then serve as a starting point for steering you toward a solution.

    You need to define your metrics before you can talk about "simplifying" or "minimum". What is the basis for comparing which of two solutions is simpler? What are the limits on the types of gates you can use and how are the total number of gates being counted?
     
  3. scubagabriella

    Thread Starter New Member

    Sep 22, 2013
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    I've been trying to do this problem for about an hour now. I think I did the truth table correctly but I'm not really sure. As for the amount of and the limits of the gates, there are none. Just to use the least amount of gates as possible.

    A_B_C_X
    0_0_0_0
    0_0_1_1
    0_1_0_0
    0_1_1_1
    1_0_0_1
    1_0_1_0
    1_1_0_1
    1_1_1_1
     
  4. WBahn

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    Mar 31, 2012
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    Your truth table is fine.

    Just use a three-input (AB+AC'+A'C) gate.

    If that's not a valid solution, then what is a "gate" for this problem?

    If you've been working at it for an hour, then show the efforts and results that hour has produced. It doesn't have to be finished or even correct, but you need to show some effort. After all, it is YOUR homework.
     
  5. abhaymv

    Active Member

    Aug 6, 2011
    104
    4

    A K-Map of your truth table yields the same expression as above. I'm pretty sure this is the most simplified form.

    Do you want to do this with NAND alone? Like WBahn said, please specify what gates you're using.

    I guess the standard way would be:

    Look at the Boolean expression. Does any part of it look familiar? Can you use a gate to substitute a part of the expression?

    What does each operator mean?

    What are the logic expressions corresponding to each gates?
     
    Last edited: Sep 23, 2013
  6. WBahn

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    Mar 31, 2012
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    The goal is to help the student proceed down a path that results in them understanding how to tackle the problem -- beginning first with clearly identifying the problem.

    By just giving them the answer (assuming the use of an XOR is allowed, which it may or may not be and which is what I was trying to get the OP to clarify), you have not helped them learn anything. You have simply given them an answer to the same type of problem that they have seen worked out before but which they haven't learned yet to work out for themselves. How is one more example going to change that -- especially when you didn't even show HOW to get that answer.
     
    Last edited: Sep 23, 2013
    abhaymv likes this.
  7. abhaymv

    Active Member

    Aug 6, 2011
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    I'm sorry about that, but I wasn't sure how to show it. I mean its pretty obvious, isn't it?

    I'm guessing if he understands the meaning of XOR, he'll know that I just substituted XOR for the corresponding expression. I didn't do anything complicated, which was why I couldn't show anything...

    I'll be more careful in the future.
     
  8. WBahn

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    Mar 31, 2012
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    Please do. But don't stress too much about it, either. We all make similar mistakes.

    One thing that I find helps a lot is to try to use the Socratic Method (and I admit that at times I tend to stick to it when it should have become obvious that it wasn't working).

    In the Socratic Method you try to ask leading questions -- ideally ones that the student can answer handily but that reveal a piece of information that they weren't focused on before.

    As an example, in this case you might have asked something like, "Which two of your terms can be represented by a single 'standard' logic gate? Is this gate one of the ones you are allowed to use?"

    That's the direction I was headed and, quite possibly, should already asked this question this way. I was perhaps too focused on getting the problem constraints clearly established and didn't see a simple way to work both sides of the street at the same time.
     
  9. abhaymv

    Active Member

    Aug 6, 2011
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    I've modified my post. Hopefully he hasn't seen the earlier one. ;)
    Perhaps you could modify my quote as well.
     
  10. WBahn

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    Mar 31, 2012
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    I'll go along -- and thanks for being understanding and conscientious.

    It's somewhat of a moot point, because your post would have been included in the e-mail notification she (I'm assuming a she based on username) received.
     
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