NEED help with Reducing switching expressions and Converting SEs into SoM and PoS

Discussion in 'Homework Help' started by pghaffari, Oct 11, 2011.

  1. pghaffari

    Thread Starter New Member

    Oct 1, 2011
    13
    0
    Please check if I did the following correctly. Thanks. Basically, #1 and #4 I need help with (those are primary) and #2,#3 i need you to check if i did it correctly.

    Reduce the following SE's to number of literals specified.
    1) abc'd + ab'c + bc'd + ab'c' + acd + a'bcd (4 Literals)

    bc'd(a+1) + ab'(c+c') + cd(a+a'b)
    bc'd + ab' + cd(a+b)
    bc'd + ab' + acd + bcd
    bd(c+c') + ab' + acd

    bd + ab' + acd (From here, I have 7 literals, and I don't know what to do. I've tried the following but i still end up with 6 literals and can't get 4)

    ab'(d+d') + bd(a+a') + acd
    ab'd + ab'd' + abd + a'bd + acd
    ad(b'+b) + ab'd' + a'bd + acd
    ad + ab'd' + a'bd + acd
    ad(1+c) + ab'd' + a'bd
    ad + ab'd' + a'bd
    a(d+d'b) + a'bd
    a(d+b) + a'bd
    ad + ab + a'bd
    ad + b(a+a'd)
    ad + ab + bd ... Stuck here.. What can i do? I've played with it for like 2 hours straight and can't figure it out. Any help would be greatly appreciated.

    Problem 2 (I finished this, please check if its correct)
    2) acb + ac'd + bc'd' + a'b'c' + ab'c'd' + bc'd (3 Literals)

    bc'(d'+d) + b'c'(ad' + a') + abc + ac'd
    bc' + b'c'(a'+d') + abc + ac'd
    bc' + a'b'c' + b'c'd' + abc + ac'd
    b(c' + ca) + a'b'c' + b'c'd' + ac'd
    b(c' + a) + a'b'c' + b'c'd' + ac'd
    bc' + ab + a'b'c' + b'c'd' + ac'd
    c'(b+b'a') + ab + b'c'd' + ac'd
    c'(b+a') + ab + b'c'd' + ac'd
    bc' + a'c' + ab + b'c'd' + ac'd
    c'(b + b'd') + a'c' + ab + ac'd
    c'(b + d') + a'c' + ab + ac'd
    bc' + c'd' + a'c' + ab + ac'd
    bc' + c'd' + c'(a'+ad) + ab
    bc' + c'd' + c'(a'+d) + ab
    a'c' + c'd + c'd' + bc' + ab
    a'c' + c'(d+d') + bc' + ab
    a'c' + c' + bc' + ab
    a'c' + c'(b+1) + ab
    a'c' + c' + ab
    c'(a'+1) + ab
    ab + c'

    Problem 3: Convert following SEs into sum of minterms
    {[(a+b+a'c')c+d]' + ab'}
    too much to type, but basically i got m(0,1,2,3,4,5,8,9,11,12) let me know if you agree with this if it disagrees ill type out what i have.

    Problem 4: Convert following SEs into product of maxterms without obtaining sum of minterms first

    xyz + yw + x'z' + xy'

    So basically to do this we just keep expanding until we get a product of maxterms? like this..:

    x(yz + y') + yw + x'z'
    x(y' + z) + yw + x'z'
    xy' + xz + yw + x'z'
    (xy' + x)(xy' + z) + (yw+x')(yw+z')
    x(xy'+z) + (yw+x')(yw+z')
    (xy' +xz) + (yw+x')(yw+z')
    ((xy'+xz)) + (yw+x'))((xy'+xz) + (yw+z'))

    I dont get what i do.. if i keep expanding it gets really complicated.. any suggestions??
     
    Last edited: Oct 11, 2011
  2. pghaffari

    Thread Starter New Member

    Oct 1, 2011
    13
    0
    EDIT: I FIGURED OUT PROBLEMS 1, 2. Please check 3, 4!
     
  3. pghaffari

    Thread Starter New Member

    Oct 1, 2011
    13
    0
    Need help with 4 please
     
  4. pghaffari

    Thread Starter New Member

    Oct 1, 2011
    13
    0
    Anyone?? :|
     
  5. Georacer

    Moderator

    Nov 25, 2009
    5,142
    1,266
    I find creating the PoS form of a Boolean expression through Boolean operations extremely difficult, mainly because it involves factorizing the expression. Factorization is a very difficult mathematical problem as is. Unless you already have the solution, it's very hard to imagine the correct steps towards the solution.
    I have roamed the internet looking for the solution to that problem several times, and each time I returned empty handed.

    I suggest forming the truth table of the expression and extracting the Maxterms from it. It violates the exercise guidelines indirectly, but I can't think of any other way.
     
  6. pghaffari

    Thread Starter New Member

    Oct 1, 2011
    13
    0
    its just a homework problem though im sure theres a simple way to do it without making truth table ?
     
Loading...