Q1 (30 pts): Use Boolean-algebraic manipulation to prove the following Boolean statements. Note a) and b)...

 

Transcribed Image Text:

Q1 (30 pts): Use Boolean-algebraic manipulation to prove the following Boolean statements. Note a) and b) are two forms of the absorption law. a) (5pts): x + xy = x b) (5pts): x(x + y) = x c) (10 pts): (x₁ + x₂)(x₁ + x3) = x₁ d) (10 pts): (x₁ + x₂ + x3 + x₂)(x₁ + x₂ + x3 + x₁) = x₁ + x₂ + x3 Q2 (10 pts): Draw two types of the AND-OR schematic for the following function: f(x, y, z) = IIM(0,3,5,6); a) Product-Of-Sum (POS) form. b) Sum-Of-Product (SOP) form. Q3 (20 pts): Develop a truth table for the following standard POS expressions: Y = (A +C)(A + B + C)(A + B+C) Q4 (40 pts): Based on the truth table developed for Y = (A +C)(A+B+C)(A+B+C), please implement the logic (1) using NAND gates only (some inputs can have invertors) and (2) using NOR gates only. Draw the schematics for both implementations. Q1 (30 pts): Use Boolean-algebraic manipulation to prove the following Boolean statements. Note a) and b) are two forms of the absorption law. a) (5pts): x + xy = x b) (5pts): x(x + y) = x c) (10 pts): (x₁ + x₂)(x₁ + x3) = x₁ d) (10 pts): (x₁ + x₂ + x3 + x₂)(x₁ + x₂ + x3 + x₁) = x₁ + x₂ + x3 Q2 (10 pts): Draw two types of the AND-OR schematic for the following function: f(x, y, z) = IIM(0,3,5,6); a) Product-Of-Sum (POS) form. b) Sum-Of-Product (SOP) form. Q3 (20 pts): Develop a truth table for the following standard POS expressions: Y = (A +C)(A + B + C)(A + B+C) Q4 (40 pts): Based on the truth table developed for Y = (A +C)(A+B+C)(A+B+C), please implement the logic (1) using NAND gates only (some inputs can have invertors) and (2) using NOR gates only. Draw the schematics for both implementations.