GATE CSE 2001 | Question: 10

Question

1. Is the $3\text{-variable}$ function $f= \Sigma(0,1,2,4)$ its self-dual? Justify your answer.
2. Give a minimal product-of-sum form of the $b$ output of the following $\text{excess-3}$ to $\text{BCD}$ converter.

Comments

plz answer part B also..

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$Remark:$ self dual function is that function, if we calculate one time dual of that function then we get the original function back.

Answer 1

a) It is a self dual function, because it satisfies both conditions of self dual fuction

            ->It should be neutral (i.e no. of minterms is equal to the no. of maxterms)

            ->The function does not contain two mutually exclusive term ( eg ABC mutually exclusive to A'B'C' , AB'C' mutually  excluseive to A'BC)

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b) Excess-3 to BCD converter

 Ref http://www.sukanta.info/wp-content/uploads/2012/05/Excess-3-code-to-bcd-converter3.pdf

Answer 2

Now to minimize the terms we have to make kmap  but how we will fill entry first see where is B3 one now according to that values put values 1 in kmap for eg: for $1000$ here B3 is 1 so in kmap put value 1 for 1011 and for 1001 is also B3 is 1 now put value 1 for 1100 .. and Make 4 kamp with respect to different output .