(Solved): please help, not sure if there is more input gates that are correct. Consider the design of two log ...

please help, not sure if there is more input gates that are correct.

Consider the design of two logic circuits that both have four inputs: A, B, C and D; and one output: X. Each circuit is implemented using 4-input AND gates (with negated inputs) and each circuit has an OR gate to generate the output. - For circuit $$1,\mathrm{X}$$ is defined to be 1 if and only if interpreting $$\mathrm{ABCD}$$ as an unsigned binary integer results in an odd number. Note $$\mathrm{A}$$ is the most significant bit, then $$\mathrm{B}$$, and so on. - For circuit $$2,\mathrm{X}$$ is defined to be 1 if and only if the total number of 1 's among $$\mathrm{A},\mathrm{B},\mathrm{C}$$ and $$\mathrm{D}$$ is even. Which of the following 4-input gates would be used in the implementation of both circuits?