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Logic gate

  1. Nov 16, 2015 #1
    1. The problem statement, all variables and given/known data
    c169c8f91af3.jpg


    2. The attempt at a solution
    Circuit:
    91e7e7e803e9.jpg

    A B G D E F C
    0 0 1 1 1 1 0
    1 1 0 1 0 1 0
    0 0 1 1 1 1 0
    1 1 0 1 0 1 0


    Answer:
    4a4a394bc57f.jpg

    Is (a) right? And any ideas what could be (b)?
     
  2. jcsd
  3. Nov 16, 2015 #2

    jedishrfu

    Staff: Mentor

    Your A and B columns should show all possible values {00, 01, 10, 11}

    The output of the D NAND gate is: A' NAND B = (A' & B)' = D

    and the F NAND gate is: A NAND B' = (A & B')'
     
  4. Nov 16, 2015 #3
    You mean I should have four columns?

    A1 0101
    A2 1010
    B1 0101
    B2 1010

    Like this?
     
  5. Nov 16, 2015 #4

    jedishrfu

    Staff: Mentor

    No, you still have an A and a B column:

    Code (Text):


    A   B
    --  --
    0   0
    0   1
    1   0
    1   1

     
     
  6. Nov 16, 2015 #5
    But how did you derive these numbers? My original 0101 in A and B I got from the inverter table. But I don't see how to get the ones you mention.
     
  7. Nov 16, 2015 #6

    jedishrfu

    Staff: Mentor

    Your A and B inputs can be any binary value so since you have two inputs you have a possibility of 4 input values to the circuit as shown in the table above.
     
  8. Nov 16, 2015 #7
    I get it now.

    So:
    Code (Text):
    A   B   G   D   E   F   C

    0   0   1   1   1   1   0
    0   1   1   0   0   1   1
    1   0   0   1   1   0   1
    1   1   0   1   0   1   0
     
  9. Nov 16, 2015 #8

    jedishrfu

    Staff: Mentor

    That's what I got too. The circuit diagram has a symmetry about it which is seen in the truth table.
     
  10. Nov 16, 2015 #9
    But what could be said about (b)? No idea about it.
     
  11. Nov 16, 2015 #10

    jedishrfu

    Staff: Mentor

    Look at the A and B inputs and then the C output doesn't that look like some gate you're familiar with?
     
  12. Nov 16, 2015 #11
    I would say the "final" truth table should include only A, B, and C.
     
  13. Nov 16, 2015 #12
    AND has 0001 at output
    OR 0111
    NOR 1000
    NAND 1110
    Inverter 10

    And I have at output 0110. The input is the same for this circuit and for AND, OR, NOR and NAND.
     
  14. Nov 16, 2015 #13
    Last edited: Nov 16, 2015
  15. Nov 16, 2015 #14
  16. Nov 16, 2015 #15
    The truth table for this problem should have three columns - two for A and B inputs, and one for the result C.
     
    Last edited by a moderator: Nov 16, 2015
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