Question 3 (30 POINTS). Please perform the required operations for each Boolean equation given in questions 3A through 3C. For each question, please use a circuit sketching tool to draw your circuit diagram. Following is a list of some freely available circuit sketching tools. You may also use another tool of your choice.

3.A.) Y = ABC + ABC i.) (3 POINTS) Simplify the Boolean equation using Boolean theorems by specifying which theorem(s) you have used. Please show your work.

ii.)	(3 POINTS) Check the simplification for correctness using a Karnaugh map. Please show your work.

iii.) (4 POINTS) Sketch a simple combinational circuit diagram for the simplified equation, i.e. after you simplify. 3.B.) Y = ABC +AB

	i) (3 POINTS) Simplify the Boolean equation using Boolean theorems by specifying which theorem(s) you have used. Please show your work. ii) (3 POINTS) Check the simplification for correctness using a Karnaugh map. Please show your work. iii) (4 POINTS) Sketch a simple combinational circuit diagram for the simplified equation, i.e. after you simplify

3.C.) Y = ABCD +ABCD +(A +B +C +D)

	i) (3 POINTS) Simplify the Boolean equation using Boolean theorems by specifying which theorem(s) you have used. Please show your work. ii) (3 POINTS) Check the simplification for correctness using a Karnaugh map. Please show your work. iii) (4 POINTS) Sketch a simple combinational circuit diagram for the simplified equation, i.e. after you simplify 4.A.) (5 POINTS) Write the Boolean equation for each output, i.e. Y and Z in this circuit. 4.B.) (15 POINTS) Simplify the Boolean equations for Y and Z in 4A using a Karnaugh map. Please show your work. Then, draw the simplified circuit again. Please use a circuit sketching tool

Please use the following truth table for Questions 1 and 2 A B C D|Y 0 1 00 0 0 1 01 0 1 0 001 1 1 1 0 0