Q.Convert $Y = AC + B\overline{C}$ into its canonical SOP form

A canonical (standard) SOP form expresses every product term over all three variables A, B, C. Expanding each term of $Y = AC + B\overline{C}$ by ANDing in the missing variable gives four distinct minterms. …

[!TLDR]

$AC = ABC + A\overline{B}C$ and $B\overline{C} = AB\overline{C} + \overline{A}B\overline{C}$, so the canonical SOP is $Y = \overline{A}B\overline{C} + A\overline{B}C + AB\overline{C} + ABC = \sum m(2,5,6,7)$.

In this Karnataka II PUC Electronics digital-logic example, a canonical (standard) SOP requires each product term (minterm) to contain all input variables, either in true or complemented form. Convert each term by ANDing it with $(X + \overline{X})$ for every missing variable $X$, then expand (A is the MSB, C the LSB).

Term 1 - $AC$ is missing B, so AND it with $(B + \overline{B})$:

Term 2 - $B\overline{C}$ is missing A, so AND it with $(A + \overline{A})$:

Combining the four minterms (all distinct, none repeated): …