Implement a Boolean function using 4 to 1 multiplexer

Discussion in 'Homework Help' started by mcc123pa, Dec 5, 2010.

  1. mcc123pa

    Thread Starter Member

    Sep 12, 2010
    40
    0
    Hi again-

    Here are the instructions to the second problem that I am wondering about:

    A combinational circuit is specified by the following Boolean function:
    F(A,B,C,D)= Ʃ(0,2,6,7,8)
    Implement the circuit using ONE 4:1 multiplexer and other necessary gates. Use A and B as MUX selection inputs. Only uncomplemented inputs are available.

    My attempt at a solution is as follows:
    A B C D F
    0 0 0 0 1
    0 0 0 1 0
    0 0 1 0 1
    0 0 1 1 0
    0 1 0 0 0
    0 1 0 1 0
    0 1 1 0 1
    0 1 1 1 1
    1 0 0 0 1
    1 0 0 1 0
    1 0 1 0 0
    1 0 1 1 0
    1 1 0 0 0
    1 1 0 1 0
    1 1 1 0 0
    1 1 1 1 0

    Above is my truth table. The problem should be fairly simple only I am confused of how to set it up with the directions saying I should only use uncomplemented inputs. That is because I got D0 = D' and D2= C'D'. How should I procede to get the correct answer? Thanks in advance for your help!
     
  2. blah2222

    Well-Known Member

    May 3, 2010
    554
    33
    F = A'B'C'D' + A'B'CD' + A'BCD' + A'BCD + AB'C'D'

    Use Shannon's Expansion to factor out select inputs:

    F = A[B'C'D'] + A'[B'C'D' + B'CD' + BCD' + BCD]
    F = A[B(0) + B'(C'D')] + A'[B(CD' + CD) + B'(C'D' + CD')]

    Tidying it up:

    F = A[B(0) + B'(C'D')] + A'[B(C) + B'(D')]

    Code ( (Unknown Language)):
    1.             AB
    2.             ||
    3. D' -------->|\
    4. C  -------->| \
    5. C'D' ------>| |-------->F
    6. 0  -------->| /
    7.             |/
     
    Last edited: Dec 6, 2010
  3. Georacer

    Moderator

    Nov 25, 2009
    5,142
    1,266
    What the instruction said is that you don't have the inputs complement ready to use and you have to use an inverter to obtain it.
    No big deal.
     
  4. mcc123pa

    Thread Starter Member

    Sep 12, 2010
    40
    0
    Thanks for the help everyone!! I really appreciate it!!
     
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