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Given the function f = x1x2x4 x2x3x4' x1'x2'x3', a straightforward implementation in an FPGA with three input LUTs requires four LUTs. Show how it can be done using only 3 three-input LUTs. Label the output of each LUT with an expression representing the logic function that it implements.
a) LUT1: x1x2, LUT2: x2x3x4', LUT3: x1'x2'x3'
b) LUT1: x1x2x4, LUT2: x2x3x4', LUT3: x1'x2'x3'
c) LUT1: x1x2, LUT2: x2x3, LUT3: x1'x2'x3'
d) LUT1: x1x2x4, LUT2: x2x3, LUT3: x1'x2'x3'

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