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Number of Essential prime implicant?

in Digital Logic
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it depends on selection of i/p.

case i) if consider '0' is first selection i/p and '1' is 2nd ...

then EPI's=3

case ii)if consider A' is first selection i/p and A is 2nd....

then EPI's=3

In this problem both are same ,other problems it may not.

In gate exam they clearly mention on selection of i/p.no need to worry.
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Output Y becomes = $\overline{B}C + AB\overline{C} + \overline{A}BC$

K-Map will be

A \ BC 00 01 11 10
0   1 1  
1   1   1

$\therefore$ EPI = 3

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3 EPI

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3 essential prime implicants

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