Givn a function \$f(w,x,y,z)=\Sigma(1,4,5,7,13)+\Sigma_\phi(0,8,9,12,15)\$
I set up a karnaugh map for it, and my question is:
Other than counting, what is the best way to calculate how many \$f\$ are there?
I know this is somewhat a combinatorics question, but since the karnaugh map works in a bit change not all combinations are valid functions.

  • \$\begingroup\$ What are Σ and Σϕ? \$\endgroup\$ – user253751 Jan 19 '16 at 8:08
  • \$\begingroup\$ Sum of products of the minterms and the dont cares of the function. \$\endgroup\$ – Yinon Eliraz Jan 19 '16 at 8:09
  • \$\begingroup\$ I don't know what that is supposed to mean. And if they're functions, why do their parameters have nothing to do with w, x, y or z? \$\endgroup\$ – user253751 Jan 19 '16 at 8:16
  • \$\begingroup\$ en.wikipedia.org/wiki/Karnaugh_map \$\endgroup\$ – Yinon Eliraz Jan 19 '16 at 8:20
  • 1
    \$\begingroup\$ I know what a Karnaugh map is. I don't know how Σ(1,4,5,7,13) is "the sum of the products of the minterms" and likewise how Σϕ(0,8,9,12,15) is "the sum of the products of the dont-cares". \$\endgroup\$ – user253751 Jan 19 '16 at 8:26

If you don't place any constraints on it, there are infinite functions, I believe.

(because \$A\overline A\$ can be added to anything, ad infinitum, for example)


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