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Synchronous non-sequential binary counter

  1. May 23, 2009 #1
    I am required to design a synchronous binary counter using jk flip-flops giving the count sequence: 0, 8,9,4,7,2,1,0

    I have derived the excitation table using 4 jk flip-flops, however when using karnaugh maps to minimise or trying to use the unminimised function in a circuit I am unable to get it working.

    Here is my excitation table:
    Code (Text):

    Present state   Next state                            Flip-flop inputs
    Q3  Q2  Q1  Q0  Q3  Q2  Q1  Q0  J3  K3  J2  K2  J1  K1  J0  K0
    0   0   0   0   1   0   0   0   1   X   0   X   0   X   0   X
    1   0   0   0   1   0   0   1   X   0   0   X   0   X   1   X
    1   0   0   1   0   1   0   0   X   1   1   X   0   X   X   1
    0   1   0   0   0   1   1   1   0   X   X   0   1   X   1   X
    0   1   1   1   0   0   1   0   0   X   X   1   X   0   X   1
    0   0   1   0   0   0   1   0   0   X   0   X   X   0   0   X
    0   0   0   1   0   0   0   0   0   X   0   X   0   X   X   1
     
    from this I have obtained the unminimised functions for each flip flop:
    ( ' denotes not )

    J3 = 'q3.'q2.'q1.'q0
    K3 = q3.'q2.'q1.q0

    J2 = q3.'q2.'q1.q0
    K2 = 'q3.q2.q1.q0

    J1 = 'q3.q2.'q1.'q0
    K1 = don't care

    J0 = q3.'q2.'q1.'q0 + 'q3.q2.'q1.'q0
    K0 = q3.'q2.'q1.q0 + 'q3.q2.q1.q0 + 'q3.'q2.'q1.q0

    Can anyone tell me what I am doing wrong? Any help would be much appreciated.

    Thanks
     
  2. jcsd
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