Logic Gates!

Logic Level 4

What is the minimum number of basic one/two input gates needed to implement the following Boolean Function?

\( F(w, x, y, z) = w'x'y'z' + wx'yz' + x'y'z' + w'x'z' + wxz + xy'z + w'xz \)


  • Basic Gates include AND, OR, and NOT only. XOR, NAND and NOR gates do not count in this problem.
  • Each AND/OR gate must only accept two inputs. Each NOT gate must only have one output.
  • Available inputs are only w, x, y, and z.

As an explicit example,

For the function \(F (x,y,z) = xy'z + xy'z' + x'y' \), this can be simplified to be \(F (x,y,z) = y' \), which means it only needs one NOT gate to have the function implemented.


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