# Logic Gates!

Logic Level 4

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

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

Clarifications:

• 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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