Determine the fixed polarity arithmetic expressions


Response to the following :

For functions in Problem 1, determine the fixed polarity arithmetic expressions, and show that the FPRM- repressions can be derived from them by recalculating the coefficients modulo 2 and replacing the operations of the addition and subtraction by EXOR.

Problem 1: How many Fixed-polarity Reed-Muller expressions there are for functions of n = 3 variables? Determine all them for the function given by the SOP-expression

f(x1,x2,x3) = x¯1x2 + x1x3 + x23 + x1x2x3,

and compare their complexities in terms of the number of non-zero coefficients.

 

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