Any function can be implemented directly as specified or as its inverted form wi

Question

Any function can be implemented directly as specified or as its inverted form with a not gate added at the final output. Assume that the circuit size is proportional to only the number of AND gates and OR gates, i.e. ignore the number of NOT gates in determining the circuit size. Determine which form of the function (the inverted or un - inverted) will result in a smaller circuit size for the following function. Give your reason and specify how many AND and OR gates are needed to implement the smaller circuit.

Explanation / Answer

Well first of all I will try to simplify the function

x'y'z'+x'y'z+xy'z+xy'z'+xyz

now

x'y'(z+z') + xy'(z+z') + xyz

now we know that z+z' will always be 1

so it can be simplified as

x'y' + xy' +xyz

y'(x+x') + xyz

F=y'+xyz

the above is the simplified version of the function

now if we use inverted logic then

(y'+xyz)'

y.(xyz)'

Seeing the above equations the uninverted form will be helpful here.

I will take two and gates and one more gate for the same.

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