Q.Draw the Logic Circuit of the following Boolean Expression: A.B + A.C

A.B + A.C = two AND gates feeding one OR gate (A fans out to both ANDs):

A ──┬─[AND]── A.B ─┐
B ──┘              ├─[OR]── F = A.B + A.C
A ──┬─[AND]── A.C ─┘
C ──┘
``` …

Concept — reading the expression as gates

In Boolean notation . is AND and + is OR, and AND binds tighter than OR. So A.B + A.C means: first form the two products A.B and A.C, then OR them. That maps directly onto hardware:

1. AND gate 1 — inputs A and B, output A.B.
2. AND gate 2 — inputs A and C, output A.C. (The same input line A branches to both AND gates.)
3. OR gate — inputs A.B and A.C, output F = A.B + A.C.

The logic circuit

A ────┬───────────┐
      │           ├─[ AND ]── A.B ──┐
B ────┼───────────┘                 │
      │                             ├─[ OR ]──── F = A.B + A.C
      └───────────┐                 │
                  ├─[ AND ]── A.C ──┘
C ────────────────┘

Gate count: 2 AND gates + 1 OR gate. The single line A fans out to both AND gates — do not draw two separate A sources.

Equivalent minimized circuit (acceptable alternative) …