Q.Convert A+BC+ $\overline{A}B$ into its canonical SOP and write the expression in min term designation.

The three-variable function $Y=A+BC+\overline{A}B$ is first simplified, then every product term is expanded to include all three variables A, B, C. …

[!TLDR]

$Y=A+BC+\overline{A}B=A+B=\Sigma m(2,3,4,5,6,7)$ over the three variables A, B, C.

Step 1 — simplify: Using the absorption identity $A+\overline{A}B=A+B$,

So the function reduces to $Y = A+B$, but it is a three-variable function (A, B, C).

Step 2 — expand each term to the missing variables (canonical SOP):

• $A = A(B+\overline{B})(C+\overline{C}) = ABC + AB\overline{C} + A\overline{B}C + A\overline{B}\,\overline{C}$.
• $B = B(A+\overline{A})(C+\overline{C}) = ABC + AB\overline{C} + \overline{A}BC + \overline{A}B\overline{C}$.

Collecting the distinct minterms:

$Y = \overline{A}B\overline{C} + \overline{A}BC + A\overline{B}\,\overline{C} + A\overline{B}C + AB\overline{C} + ABC.$ …