Simplify using k map:

(A’ + B’ + D’) (A + B’ + C’) (A’ + B + D’) (B + C’ + D’)

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Given Expression is

Y = (A’ + B’ + D’)(A + B’ + C’)(A’ + B + D’)(B + C’ + D’)

We will simplyfy this expression using Sum of Product (max-terms). First we will simply each expression as below:

(A’ + B’ + D’) = (A’ + B’ + CC’ + D’)

= (A’ + B’ + C + D’) (A’ + B’ + C’ + D’)

(A + B’ + C’) = (A + B’ + C’ + DD’)

= (A + B’ + C’ + D) (A + B’ + C’ + D’)

(A’ + B + D’) = (A’ + B + CC’ +  D’)

= (A’ + B + C +  D’) (A’ + B + C’ +  D’)

(B + C’ + D’) = (AA’ + B + C’ + D’)

= (A + B + C’ + D’) (A’ + B + C’ + D’)

Now, Final Expression be

Y = (A’ + B’ + C + D’) (A’ + B’ + C’ + D’) (A + B’ + C’ + D) (A + B’ + C’ + D’) (A’ + B + C +  D’) (A’ + B + C’ +  D’) (A + B + C’ + D’) (A’ + B + C’ + D’)

Y = ∏(13, 15, 6, 7, 9, 11, 3)

Y = ∏(3, 6, 7, 9, 11, 13, 15)

Now, Implementing using k-map, we get

Max-term k-map

From k-map, we get final expression as:

Y = (A’ + D’) (C’ + D’) (A + B’ + C’)

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