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Computer science - implement a function

  1. Sep 28, 2009 #1
    Not sure where to put this thread. I'll just post it here. I need help with the following:

    Can someone tell me how to do this? I have no idea. I'd really appreciate it.
     
  2. jcsd
  3. Sep 28, 2009 #2

    CRGreathouse

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    What are you allowed to use other than 3-to-8 decoders -- OR gates?
     
  4. Sep 28, 2009 #3
    Probably....these won't work?
     
  5. Sep 28, 2009 #4

    CRGreathouse

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    Without building it, I would guess that it could be done with two 3-to-8s if you allow ORs, but it certainly requires 3+ if you don't.
     
  6. Sep 29, 2009 #5
    a 3 to 8 decoder can implement a 2 or 3 input NOR gate. You can build all possible
    logical circuits with NOR gates
     
  7. Sep 29, 2009 #6

    CRGreathouse

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    Yes, but you'll need many 3-to-8 decoders if you build it this way! The question asked for the minimal number of decoders, so I had to know the actual requirements.
     
  8. Sep 29, 2009 #7

    uart

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    Yes I can do it with just two 3-to-8 decoders plus three 2-input OR gates. I've been a bit reluctant to contribute to this thread or post a complete solution becasue it certainly looks a bit like homework.

    Xodox, tell us what you already know or have done. Do you know what a "min-term" is? Do you know how to construct a boolean function as a sum of min-terms? Have you learnt that a decoder can be considered as a "min-term generator"?
     
  9. Sep 29, 2009 #8

    CRGreathouse

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    Good for you. It was easy enough for me to do it with only two 3-to-8s but I used more ORs.

    I wonder if 3 is the minimum number of ORs with 2 decoders.
     
  10. Sep 29, 2009 #9

    uart

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    Hi CRGreathouse, I think I know where you needed more OR gates. The A’CD + AC’D’ part is easy right, just two min terms of (A,C,D); but the A’B + AB’ may require more min terms and hence more OR gates depending on how you approach it.

    You can however easily make A’B + AB’ with only two min terms of (A,B,X) if you make an appropriate choice for "X". Hint: think about boolean constants rather than only variables. :)
     
  11. Sep 29, 2009 #10

    CRGreathouse

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    Nah, my approach was different. But thanks for the tip.
     
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