1a. Develop the logic circuit necessary to meet the following requirements. A battery powered lamp in a room is to be operated from two switches, one at the back door and one at the front door. The lamp is to be ON if the FRONT switch is ON and BACK switch if OFF, or if the FRONT switch is OFF and the BACK switch is ON. The lamp is to be OFF if both switches are OFF or if both switches are ON. Let a HIGH output represent the ON condition and LOW output represents the OFF conditions. (10 marks)

b. An industrial system has three sensors which are sensor A, sensor B, and sensor C to determine if a process is working correctly. A warning light (Q) should come on if: -Sensors B and C are activated, but A are not activated. -Sensors A and B are activated, but C is not activated. -Sensors A, B and C are not activated. -Sensors A, B and C are activated.

i.Based on the information stated, develop a truth table for this system (2 marks)

ii.Write the Boolean expression of this system in the sum-of products (SOP) form and product of sum (POS) form. (2 marks)

iii.Deduce the sum-of-products function for this system using a K-map. (3 marks)

iv.Sketch a logic circuit using only two input AND, OR and NOT gates, which implements the expression derived in Question 2b (iii). (3 marks)