Q.Convert $AB + \overline{C}$ into canonical SOP.

Each product term in a canonical SOP must contain all three variables A, B, C. The incomplete terms are expanded by multiplying with $(X + \overline{X})$ for every missing variable and collecting the distinct minterms. …

[!TLDR]

Expanding each term to three variables gives $AB + \overline{C} = \sum m(0,2,4,6,7)$.

A canonical (standard) SOP expression is one in which every product term is a minterm — it contains all the variables of the function, each appearing once (true or complemented). The given expression $Y = AB + \overline{C}$ has terms missing variables, so each is expanded by AND-ing with $(X + \overline{X}) = 1$ for each absent variable.

Expand $AB$ (missing C):

$AB = AB(C + \overline{C}) = ABC + AB\overline{C}$ → minterms $m_7, m_6$.

Expand $\overline{C}$ (missing A and B):

$\overline{C} = (A + \overline{A})(B + \overline{B})\overline{C} = AB\overline{C} + A\overline{B}\,\overline{C} + \overline{A}B\overline{C} + \overline{A}\,\overline{B}\,\overline{C}$ → minterms $m_6, m_4, m_2, m_0$. …