2 bit binary counter karnaugh diagram

Discussion in 'Homework Help' started by hadoque, Nov 8, 2009.

  1. hadoque

    Thread Starter Member

    Jul 24, 2007
    10
    0
    Hi
    I'm supposed to design a 2 bit binary counter with an extra input, x, to decide whether it should count up or down (x=1 counts up). The design uses two D-flip-flops.
    To help I got a couple of truth tables to fill in. The first is for both flip-flops, D1 and D2. Then this one is split to two separate tables, for each flip-flop.
    q1 is the output of the D1 flip-flop and so forth.
    This is how I filled the tables:
    Code ( (Unknown Language)):
    1.  
    2. q1q2|x=0|x=1
    3. ____|___|___
    4. 00  | 11|01
    5. ____|___|___
    6. 01  | 00|10
    7. ____|___|___
    8. 11  | 10|00
    9. ____|___|___
    10. 10  | 01|11
    11. ____|___|___
    12.  
    13.      D1 D2
    14.  
    15. q1q2|x=0|x=1
    16. ____|___|___
    17. 00  |  1|  1
    18. ____|___|___
    19. 01  |  0| 0
    20. ____|___|___
    21. 11  |  0| 0
    22. ____|___|___
    23. 10  |  1| 1
    24. ____|___|___
    25.  
    26.      D1
    27.  
    28. q1q2|x=0|x=1
    29. ____|___|___
    30. 00  | 1 |0
    31. ____|___|___
    32. 01  | 0 |1
    33. ____|___|___
    34. 11  | 1 |0
    35. ____|___|___
    36. 10  | 0 |1
    37. ____|___|___
    38.  
    39.      D2
    40.  
    When I collect the ones to make the boolean functions, I get:

    Code ( (Unknown Language)):
    1.  
    2. D1 = q1' + q2'
    3. D2 = x'q1'q2' + xq1'q2 + x'q1q2 + xq1q2'
    4.  
    But D2 equals 1, so I must have made an error somewhere. Please help.
     
  2. Thav

    Member

    Oct 13, 2009
    82
    0
    How does D2 equal 1? It looks correct to me. Your equation for D1 is off, however.
     
  3. hadoque

    Thread Starter Member

    Jul 24, 2007
    10
    0
    Because I suck at Boolean algebra.. ;)
    The correct answer should be:
    D1 = q2'
    D2 = (x(XOR)q1(XOR)q2)'
    but I also separated the tables wrong, so D1=D2, and vice versa.
     
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