Pos (/a+b)(a+/b)(/b+c)

Discussion in 'Homework Help' started by GGerardo2010, Dec 11, 2010.

  1. GGerardo2010

    Thread Starter New Member

    Dec 11, 2010
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    0
    I am working on this circuit and I have a few questions.

    First I have (/A+B)(A+/B)(/B+C)

    I want to use all NOR gates for this project.

    ABC F
    000 1
    001 1
    010 0
    011 1
    100 0
    101 1
    110 1
    111 1

    This is my truth table so I made the design with NAND gates which was wrong I need to create design with all NOR gates, I read somewhere that I need to use inverters before and after each gate.

    How can I just use all NOR gates and do I use inverters or can I short the NOR gates as I go along?

    I am not sure if the truth table is right?

    How can the equation be solved, direct method or Demorgan's theorem?

    Can anyone help?

    G.
     
  2. Wendy

    Moderator

    Mar 24, 2008
    20,765
    2,536
    Another way to go about it is to convert the gates in the layout. You will likely have to have inverters (which is a NOR gate with the inputs connected), but it is actually pretty easy.

    [​IMG]
     
  3. GGerardo2010

    Thread Starter New Member

    Dec 11, 2010
    4
    0
    Is this truth table correct? If so then its my design that is not working. I did make a design using NAND gates which that worked fine it follows the truth table, but I could be wrong.

    Thanks!
     
  4. tyblu

    Member

    Nov 29, 2010
    199
    16
    Just verify it.. feed in inputs, calculate output.
     
  5. GGerardo2010

    Thread Starter New Member

    Dec 11, 2010
    4
    0
    I think that is the question, how to verify it multiply the variables together or by inputting zeros to the location of the variables.

    (/A+B) is located @ 011, 010
    (A+/B) is located @ 100, 101

    (/B+C) is located @ 001. 101

    In the POS method do you place a 1 in the KMAP to these locations or place a 0 where these variables are located?

    The designing the circuit is no problem its the equation is what I am concerned about.

    Can some tell me if the truth table is correct or is the a simpler way to do this?
     
  6. tyblu

    Member

    Nov 29, 2010
    199
    16
    It's just "plug and chug":

    F(A,B,C) = (\not A + B)(A + \not B)(\not B + C)
    F(0,0,0) = (1 + 0)(0 + 1)(1 + 0) = (1)(1)(1) = 1
    F(0,0,1) = (1 + 0)(0 + 1)(1 + 1) = (1)(1)(1) = 1
    F(0,1,0) = (1 + 1)(0 + 0)(0 + 0) = (1)(0)(0) = 0
    F(0,1,1) = (1 + 1)(0 + 0)(0 + 1) = (1)(0)(1) = 0
    F(1,0,0) = (0 + 0)(1 + 1)(1 + 0) = (0)(1)(1) = 0
    F(1,0,1) = (0 + 0)(1 + 1)(1 + 1) = (0)(1)(1) = 0
    F(1,1,0) = (0 + 1)(1 + 0)(0 + 0) = (1)(1)(0) = 0
    F(1,1,1) = (0 + 1)(1 + 0)(0 + 1) = (1)(1)(1) = 1
     
  7. GGerardo2010

    Thread Starter New Member

    Dec 11, 2010
    4
    0
    I have done that so many times I thought I was wrong! I thought I need to do something else like foil the variables out term by term.

    Thank you. let me see I'll post the design up when I am done.
     
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