1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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):

    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.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook