(Solved): solve the first one using bolean expressions with steps Problem 3. Simplify the following Boolean al ...

Problem 3. Simplify the following Boolean algebraic expressions and draw a block diagram of the circuit for each simplified expression using AND and OR gates. (a) ${\mathrm{AB}}^{?}{\mathrm{C}}^{?}+{\mathrm{A}}^{?}{\mathrm{B}}^{?}{\mathrm{C}}^{?}+{\mathrm{A}}^{?}{\mathrm{BC}}^{?}+{\mathrm{A}}^{?}{\mathrm{B}}^{?}\mathrm{C}$ (b) ${\mathrm{A}}^{?}\mathrm{BC}+{\mathrm{AB}}^{?}\mathrm{C}+{\mathrm{A}}^{?}\mathrm{BC}+{\mathrm{ABC}}^{?}+{\mathrm{AB}}^{?}{\mathrm{C}}^{?}+{\mathrm{A}}^{?}{\mathrm{BC}}^{?}+{\mathrm{A}}^{?}{\mathrm{B}}^{?}{\mathrm{C}}^{?}$ (c) $(A+B+C)\left(A+B^{?}+C^{?}\right)\left(A+B+C^{?}\right)\left(A+B^{?}+C\right)$ Problem 4. Prepare the Truth Table for the following Boolean expressions: (a) $\mathrm{XYZ}+{\mathrm{X}}^{?}{\mathrm{Y}}^{?}{\mathrm{Z}}^{?}$ (b) $(A+B)(A+C)\left(A^{?}+B^{?}\right)$ (c) $\mathrm{AB}+\mathrm{AC}$ Problem 5. Write the Boolean expression (in Sum of Products form) for the logic circuit that will have a loutput when $\mathrm{X}=0,\mathrm{Y}=0,\mathrm{Z}=1$ and $\mathrm{X}=1,\mathrm{Y}=1,\mathrm{Z}=0$, and a zero $(0)$ output for all other input states. Draw the logic diagram for this circuit. Problem 6. Draw a logic diagram of your own provided that it has at least three inputs and three gates (NOTs are not counted). Write the Boolean expression (function) and generate the truth table for this circuit.