Implementing a circuit with a decoder

Discussion in 'Homework Help' started by mcc123pa, Dec 5, 2010.

  1. mcc123pa

    Thread Starter Member

    Sep 12, 2010

    Here are the directions to the problem that I am stumped on:

    A combinational circuit is specified by the following Boolean function:
    F(A,B,C,D) = Ʃ(0,2,6,7,8)

    A) Implement the circuit with a decoder and external gates.

    Below is my attempt at a solution:

    step 1: I transfer this expression to a four variable K-map and get the following optimized expression:
    f= b'c'd+a'cd'+a'bc

    step 2: I have to introduce all four variables to each term so I perform the following expansion:

    F= b'c'd'(a+a')+a'cd'(b+b')+a'bc(d+d')
    F= ab'c'd'+a'b'c'd'+ a'bcd'+a'b'cd'+a'bcd+a'bcd'
    (8) (0) (6) (13) (7) (6)

    step 3: I set up the decoder with the external OR gate and connect outputs 8, 0, 6, 13, and 7 to it.

    My question is, did I do it correct up to here? If I did, should I connect 6 to the OR gate twice? Or do I need to look in a new direction to finish this problem? Please advise either way. Thanks in advance for your answers!!
  2. blah2222

    Well-Known Member

    May 3, 2010
    Yeah, that's right. Since the question didn't specify what type of decoder to use, you can just assume a 4:16 decoder with an enable input. Since the function is true at minterms: 0, 2, 6, 7, and 8, just hook all the corresponding output wires up into an OR gate, and don't connect the other outputs, leaving them with high impedance outputs.
  3. Georacer


    Nov 25, 2009
    What you did there was totally meaningless. You started from the minterms stated as a sum, got them through a K-map, simplified it and re-expanded them, just to get to them again and wrong too?!

    Just hook up your OR gate in the decoder's outputs 0,2,6,7,8 as your problem initially states.
  4. mcc123pa

    Thread Starter Member

    Sep 12, 2010
    Thanks for the replies and help everyone!!