I have got some silly task, but I am quite confused.
Need to minimize function.
$f(x_1,x_2,x_3,x_4)=x_1x_2+x_1x_3+x_1x_4+x_2x_3+x_2x_4.$
Thanks.
Sorry for my English. Minimize Boolean function
I have got some silly task, but I am quite confused.
Need to minimize function.
$f(x_1,x_2,x_3,x_4)=x_1x_2+x_1x_3+x_1x_4+x_2x_3+x_2x_4.$
Thanks.
Sorry for my English. Minimize Boolean function
If I understand the notation here correctly, a Karnaugh map looks something like this:
x1x2 x1|x2 |x1|x2 |x1x2 x3x4 X X X |x3x4 X X X |x3|x4 X x3|x4 X X X
where |xn indicates the negation of xn, and xnxm indicates the conjunction of xn and xm, and the X's represent where and only where such a conjunction evaluates to "1" (e. g. with the "X" at the intersection of x1x2 and x3x4, we have "x1x2x3x4" evaluating to "1"). If you want a minimal disjunctive normal form, you already have the unique disjunctive normal form right there, there doesn't exist anything to minimize, unless I've made a mistake here.
Do you mean to reduce the form? i.e. something like $ \begin{eqnarray} f(x_1,x_2,x_3,x_4) &=& x_1x_2+x_1x_3+x_1x_4+x_2x_3+x_2x_4 \nonumber \\ &=& x_1(x_2+x_3+x_4)+x_2(x_3+x_4) \nonumber \\ &=& x_1x_2+(x_1+x_2)(x_3+x_4) \end{eqnarray}$
Type $\rm minimize\ boolean$ into a search engine and you'll be directed to lots of webpages that may help. Another keyphrase is $\rm Karnaugh\ map$ This will lead you to http://en.wikipedia.org/wiki/Karnaugh_map among other places.