Boolean function using NAND gates

Discussion in 'Homework Help' started by maam, Nov 4, 2014.

  1. maam

    Thread Starter New Member

    Nov 4, 2014
    3
    0
    Hi,
    Can anyone help me in implementation of Boolean Functions using NAND gates.
    The function is D(A +B(C+A') + B' )
    Thanks.
     
  2. Papabravo

    Expert

    Feb 24, 2006
    10,144
    1,790
    What would be the first step? How about a truth table or the canonical SOP form.
     
  3. maam

    Thread Starter New Member

    Nov 4, 2014
    3
    0
    Can I do expand it and then apply DeMorgan's theorem
    Something like- ( (DA + DBC) + (DBA' + DB') ) ''
    ((DA+BC)'. (DBA' +DB')')'
    ( (DA)'. (BC)'. (DBA')'. (DB')')'

    Now, I can implement using NAND gates...
    Is this the correct way?
     
  4. WBahn

    Moderator

    Mar 31, 2012
    17,747
    4,796
    You need to clarify what your constraints are. Are you restricted to two-input NAND gates (a very common constraint for these types of problems), or can you use n-input NAND gates?

    In your work, what happened to the D in your DBC term?
     
  5. maam

    Thread Starter New Member

    Nov 4, 2014
    3
    0
    Sorry, accidentally missed it....
    The final expression would be
    ( ( DA)'. (DBC)'. (DBA')'. (DB')' ) '

    Using three-input NAND gate, I think it can be implemented directly now...right? (Its a new course for me, I am still trying to get to the basics)
    But can this be done using two-input NAND gate? How will I do it?
     
  6. WBahn

    Moderator

    Mar 31, 2012
    17,747
    4,796
    Actually, your expression reflects the use of two 2-input NAND gates, two 3-input NAND gates, and one 4-input NAND gate. And of course you also need some inverters, but those are trivial to make with a NAND gate, right?

    ANY logic circuit can be implemented using nothing but 2-input NAND gates (or 2-input NOR gates, or a couple of other single 2-input logic gate options).

    In this case, all you need to focus on is how to implement a 3-input NAND gate and a 4-input NAND gate using just 2-input NAND gates. To do that, consider how to make multi-input AND gates from 2-input AND gates and how to make a 2-input AND gate from 2-input NAND gates.
     
Loading...