1. The problem asks to draw circuit diagrams for three Boolean expressions without simplifying them. 2. Boolean expressions use variables (A, B, C) and operations: NOT (̅), AND, OR. 3. For each expression, we translate the formula directly into logic gates: 3.1 Expression 3.1.1: $$F = (\overline{A} + \overline{B} + C)(A\overline{B}) + \overline{(A + \overline{B})}$$ - Step 1: Identify NOT gates for $\overline{A}$ and $\overline{B}$. - Step 2: Use OR gate for $(\overline{A} + \overline{B} + C)$. - Step 3: Use AND gate for $(A\overline{B})$. - Step 4: Use AND gate to combine the outputs of steps 2 and 3. - Step 5: Use OR gate for $(A + \overline{B})$, then NOT gate for its complement. - Step 6: Use OR gate to combine the result of step 4 and step 5. 3.2 Expression 3.1.2: $$F = (\overline{A}B + C) + (AB + \overline{B}\overline{C})$$ - Step 1: NOT gates for $\overline{A}$, $\overline{B}$, and $\overline{C}$. - Step 2: AND gates for $\overline{A}B$, $AB$, and $\overline{B}\overline{C}$. - Step 3: OR gates to combine $\overline{A}B$ and $C$, and separately $AB$ and $\overline{B}\overline{C}$. - Step 4: OR gate to combine the two OR outputs. 3.3 Expression 3.1.3: $$F = A\overline{B}\overline{C} + ABC + (A + BC)$$ - Step 1: NOT gates for $\overline{B}$ and $\overline{C}$. - Step 2: AND gates for $A\overline{B}\overline{C}$, $ABC$, and $BC$. - Step 3: OR gate for $(A + BC)$. - Step 4: OR gate to combine all three terms. Each circuit diagram consists of NOT, AND, and OR gates connected exactly as per the expressions without simplification.