Generate lowest cost two level circuit

Discussion in 'Homework Help' started by nyasha, Oct 7, 2009.

  1. nyasha

    Thread Starter Active Member

    Mar 23, 2009
    90
    1
    Given the following function generate the lowest cost two level circuit using nand gates only

    f(x_{3},x_{2},x_{1},x_{0})=\sum(0,2,8,9,10,13)+D(1,3,6,7)

    My attempt to solution:

    I used Karnaugh's map to simplify to

    f=\bar x_{0}\bar x_{1}+x_{0}\bar x_{1}\bar x_{2}+x_{0}\bar x_{2}x_{3}+\bar x_{1}x_{2}\bar x_{3}

    \bar f=\bar{\bar x_{0}\bar x_{1}+x_{0}\bar x_{1}\bar x_{2}+x_{0}\bar x_{2}x_{3}+\bar x_{1}x_{2}\bar x_{3}}

    applied demorgan's theorem

    \bar f= x_{0}x_{1}\cdot\bar x_{0} x_{1} x_{2}\cdot\bar x_{0} x_{2}\bar x_{3}\cdot x_{1}\bar x_{2}x_{3}



    Guys l get stuck here.......i don't know if this is the lowest cost two level circuit ?
     
    Last edited: Oct 7, 2009
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