Digital Logic Circuit

Discussion in 'Homework Help' started by copper_pipe, Oct 12, 2017.

  1. copper_pipe

    Thread Starter New Member

    Sep 30, 2014
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    Hi all,

    Have a few problems with my assignment.

    Circuit is as follows:
    [​IMG]

    Ive derived a truth table and come up with this :

    [​IMG]
    Can someone verify if the above is correct?

    Ive then got these 2 logic expressions :

    Y = A'D' + C'D' + B'D'
    Z = D+ B

    What I want to know is (if the above is correct) Is it possible to implement the above circuit using fewer logic gates?
     
  2. copper_pipe

    Thread Starter New Member

    Sep 30, 2014
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    0
    [​IMG]

    This is the correct circuit
     
  3. dl324

    AAC Fanatic!

    Mar 30, 2015
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    If the complemented inputs are available, how many gates does your solution use? How many gates were used in the original circuit?
     
  4. copper_pipe

    Thread Starter New Member

    Sep 30, 2014
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    The circuit provided uses 3 logic gates as shown above.

    I think I need a minimum 3 gates so therefore it would not be possible to implement the circuit with a few number of gates
     
  5. dl324

    AAC Fanatic!

    Mar 30, 2015
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    I count at least 5...
     
  6. copper_pipe

    Thread Starter New Member

    Sep 30, 2014
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    Can you explain?

    I see an AND, NOR and OR
     
  7. dl324

    AAC Fanatic!

    Mar 30, 2015
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    I was referring to your solution.

    The Y expression is 4 gates, the Z expression is 1 gate; 4 + 1 = 5.
     
  8. copper_pipe

    Thread Starter New Member

    Sep 30, 2014
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    Could the Y be simplified to ABCD' ?
     
  9. WBahn

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    Mar 31, 2012
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    Part of the issue is what counts as one gate? Does a three input AND gate count as a single gate?
     
  10. copper_pipe

    Thread Starter New Member

    Sep 30, 2014
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    Yes it would.
     
  11. WBahn

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    That's a shame because it is a poor metric, both in terms of real estate (number of transistors), and speed (propagation delay). But if it's the metric you have to work with, then it is what it is.
     
  12. WBahn

    Moderator

    Mar 31, 2012
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    You tell us. ABCD' says that in order for Y to be HI, that A, B and C must be HI and D must be LO. Is that what you need for the Y signal?
     
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