Homework: Digital Logic Answers

 

  1.  
    A    		  
    B    		  
    C    		  
    F
    0 0 0 0
    0 0 1 1
    0 1 0 0
    0 1 1 0
    1 0 0 1
    1 0 1 1
    1 1 0 1
    1 1 1 0

    2.  

  2. X Y Z F
    0 0 0 1
    0 0 1 1
    0 1 0 1
    0 1 1 1
    1 0 0 0
    1 0 1 1
    1 1 0 0
    1 1 1 1

    3.  

  3. A B + A B which can be simplified to B
    Either of the following is correct.





  4. The function is A B C + A B C + A B C which can be simplified to A B C + B C.


  5. F1 = w x y z + w x y z + w x y z + w x y z + w x y z + w x y z + w x y z + w x y z
        = w x + x z

    F2 = w x y z + w x y z + w x y z + w x y z + w x y z + w x y z
        = w x + w x z

    6.  

    R(S + ST) + RT = R S + R S T + RT


  6. X Y D0 D1 D2 D3
    0 0 1 0 0 0
    0 1 0 1 0 0
    1 0 0 0 1 0
    1 1 0 0 0 1

  7. X Y Z D0 D1 D2 D3 D4 D5 D6 D7
    0 0 0 1 0 0 0 0 0 0 0
    0 0 1 0 1 0 0 0 0 0 0
    0 1 0 0 0 1 0 0 0 0 0
    0 1 1 0 0 0 1 0 0 0 0
    1 0 0 0 0 0 0 1 0 0 0
    1 0 1 0 0 0 0 0 1 0 0
    1 1 0 0 0 0 0 0 0 1 0
    1 1 1 0 0 0 0 0 0 0 1

  8. To choose between 32 inputs we need 5 control lines, since 25 = 32.

  9. A B (1) (2) (3) Sum Carry
    0 0 1 1 1 0 0
    0 1 1 1 0 1 0
    1 0 1 0 1 1 0
    1 1 0 1 1 0 1

    The column for Sum is the same as A XOR B and the column for Carry is the same as A B, thus this circuit is a valid implementation of a half adder.

    1. F = X Y Z + X Y Z + X Y Z + X Y Z

    2.  
      X      		  
      Y      		  
      Z      		  
      F
      0 0 0 1
      0 0 1 0
      0 1 0 0
      0 1 1 1
      1 0 0 0
      1 0 1 1
      1 1 0 1
      1 1 1 0

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