Convert AB + \(\bar C\) into canonical SOP.

1.	Convert AB + \(\bar C\) into canonical SOP.
Answer» Y = AB + \(\bar C\) = AB(C + \(\bar C\)) + \(\bar C\)(A + \(\bar A\))(B + \(\bar B\)) = ABC + AB\(\bar C\) + (\(\bar C\)A + \(\bar C\)\(\bar A\))(B + \(\bar B\)) = ABC + AB\(\bar C\) + \(\bar C\)AB + \(\bar C\)A\(\bar B\) + \(\bar C\)\(\bar A\)B + \(\bar C\)\(\bar B\)\(\bar A\) = \(\bar A\)\(\bar B\)\(\bar C\) + \(\bar A\)B\(\bar C\) + A\(\bar B\)\(\bar C\) + AB\(\bar C\) + ABC.

Answer»

Y = AB + \(\bar C\) = AB(C + \(\bar C\)) + \(\bar C\)(A + \(\bar A\))(B + \(\bar B\))

= ABC + AB\(\bar C\) + (\(\bar C\)A + \(\bar C\)\(\bar A\))(B + \(\bar B\))

= ABC + AB\(\bar C\) + \(\bar C\)AB + \(\bar C\)A\(\bar B\) + \(\bar C\)\(\bar A\)B + \(\bar C\)\(\bar B\)\(\bar A\)

= \(\bar A\)\(\bar B\)\(\bar C\) + \(\bar A\)B\(\bar C\) + A\(\bar B\)\(\bar C\) + AB\(\bar C\) + ABC.

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