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Homework Help: Simple boolean simplification - can i simplify it further?

  1. Mar 15, 2007 #1
    1. The problem statement, all variables and given/known data

    F(A,B,C,D) = (sum of) m (2,3,5,7,11,13)
    Design a two level network to implement the above sum of products:

    2. Relevant equations

    F(A,B,C,D) = (sum of) m (2,3,5,7,11,13)

    3. The attempt at a solution
    Code (Text):

    K-map
    ___Ab
    CD|00..01..11..10
    00|
    01|1...1....1
    11|1...1.........1
    10|
     
    My attempted solution:
    F = CA' + CDB + CD'B'
    F = CA' + C (DB + D'B')
    F = CA' + C(D xor B)'
    F = CA' + CD xor CB'

    now can i factor out the C? This has to be two level so I'm thinking it'd take up two different blocks of logic gates.

    Any help?
     
  2. jcsd
  3. Mar 22, 2007 #2
    What is a two level network may I ask?
     
  4. Mar 23, 2007 #3
    the last line of it should be: F = C (A' + D xor B')

    Since all have C in common. I'm probably wrong though.
     
  5. Mar 24, 2007 #4
    OK. I found what the definition of a two-level circuit is: the implementation of a Boolean function with NAND gates is simplest if the function is in sum-of-products form. This form corresponds to a two-level circuit.

    So, as a sum of products, I get that F = BC'D + A'BD + B'CD + A'B'C. You should be able to quickly draw the two-level circuit from it using NAND gates without any problems.
     
  6. Mar 25, 2007 #5
    thanks a tonne i managed to figure it out a while back.
    thanks
     
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