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Math Help - What would a logic block diagram look for this Boolean function?

  1. #1
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    What would a logic block diagram look for this Boolean function?

    f(A,B,C,D)=ABC+D+AC+B+D

    This might be tedious to describe but this is what I've worked out.My guess is that it's look like the

    top one is an AND gate with a not gate on the third (letter C) "prong" into it and a not gate on it's

    end (ABC).Below that is a "one prong" OR gate (D).Below that one is a "two prong" AND gate with

    a not gate on the lower prong.Below that one is an OR gate that is two pronged with a not gate on

    the lower one with a "D".Below that is an AND gate with not gates going into both the (B and D)

    prongs.Is this right?.

    My personal way of describing them AND gate=semi circle

    NOT gate=arrowhead
    OR=mitre/clerical headwear
    Attached Thumbnails Attached Thumbnails What would a logic block diagram look for this Boolean function?-lbd4q4.png   What would a logic block diagram look for this Boolean function?-lbd4q4.png  
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  2. #2
    MHF Contributor
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    Re: What would a logic block diagram look for this Boolean function?

    Hey xods.

    For your function, one decomposition is

    f(A,B,C,D)=ABC+D+AC+B+D
    = (A*B*C)+D+(AC)+(B+D)
    = [(A*{B*C})+(AC)]+[(B+D)+D]

    Where the () brackets are applied first and then the [] and the final result is the + of these two inputs. With regards to the the first operation involving A, B, and C, this is just two and gates with one result fed into the other (first operation is with {}).

    The only thing though that needs to be asked are the following:

    1) Do you need to use specific kinds of gates (usually one specific gate where you build the others and the results from these)?
    2) Do you need to optimize either the expression or the circuits to use the minimum number of gates (given a certain set of gate choices)?

    If the above don't apply then you can come up with a few different ways of doing the same thing that are all the right answer.

    Your relationship is [(DABC)+(A+D)][C+B] = (DAB)+(CA+CD)+(BA+BD) which doesn't quite look right.
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