Identify the function f3

Question

The given logic circuit is realizing the boolean function  and function 

Identify the function f3(A,B,C,D)

Answer given is 

Comments

they should give f1, otherwise left this question !

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yes, f1 is not given.
okay.

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f2=$\sum m(4,5,6,7,8,9,10,11,13)$

f=$\sum m(1,4,5,8,10,12,14,15)$

6,7,9,11,13 is not in f so it can't be in f1 so f1=$\sum m(5,8,10)$

now f1.f2=$\sum m(4,5,8,10)$

f=f1.f2+f3'

f3=$\prod M(1,12,14,15)$ remaining are don't care

Answer 1

f is one if either f3 is 0 or f1&f2 both are one..

since f2=(4,5,6,7,8,9,10,11,13)

here only 4,5,8.10 are common minterms that means maximally these minterms can participate to make f =1 by (f1&f2) both.,becoz it is AND gate

therefore f3' has to be one one 1,12,14,15 )

since answer is given in maxterms hence it is f3=M(1,12,14,15).D(4,5,8,10)