Hello, I have two boolean expressions and their simplified versions. Please show steps to get to the simplified versions.

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Truth table Output 0 0 0 0 0 40 0 DNF (with ~) = ~a-b-c~d + ~a-b-cd + ~a-bcd +-ab-cd + ~abc-d + a~b-c-d + a-bc~d + ab-cd + abc~d + abcd DNF (with overline) = abcd + abcd + abcd + abcd + abcd + abcd + abcd + abcd + abcd + abcd CNF (with ~) = (a + b + ~c + d) (a + ~b + c + d) (a + ~b + ~c + ~d) (-a + b + c + ~d) (-a + b + ~c + ~d) (~a + ~b + c + d) CNF (a + b + c + d) (a + b + c + d) (a + b + c + d) (a + b ++) (a + b+e+d) - - (with overline) - (a+b+c+ d) Some minimal forms exist Minimal Form (with ~)- -a-bd +bc-d + abd + a-b-d+-a-cd + a bc