Page 95 - ComputerScience_Class_11

8. Write the Boolean expression for the following logic circuit:
a. ?1? b. ?2? c. ?3?
?1?
A ?3?

B ?2?

C
9. Draw the logic circuit diagram of the following boolean expression:
a. (A+B)'.(B+C)'.(C+A)'
b. (A'.B + B'.C + C'.A)
c. (A+B+C)'.B'C'
d. (A'.B' + A.B)+(A.B)'
e. A'.B+A.(B+B'.C)

D. Higher Order Thinking Skills (HOTS)
1. Explain how the NOR gate can be used in designing a secure alarm system. The alarm should only activate when a specific
combination of sensors (e.g., window, door and motion detectors) is triggered. How would the NOR gate be applied to achieve
this?
2. Apply Boolean algebra to simplify the following expression: (A ∧ B) ∨ (A ∼B). What is the simplified form and what does
it represent?

E. Case study-based questions.
An industrial conveyor belt system is designed to automatically control the conveyor motor based on several sensors and control
buttons. The system needs to handle four main inputs and produce one output, which is the motor’s running state.
The following components are involved in the operation:
• Start button (S): This button is used to start the conveyor belt. It is pressed to set the input S to 1.
• Emergency stop (E): This button is used to stop the conveyor belt. It is normally closed and only opens (E = 1) when pressed.
• Object sensor at end (O): This sensor detects whether there is an object at the end of the conveyor belt. If an object is detected,
O = 1; otherwise, O = 0.
• Overload sensor (L): This sensor detects whether the conveyor belt is overloaded. If an overload is detected, L = 1; otherwise,
L = 0.
The motor (M) should run based on the following conditions:
• The Start button must be pressed (S = 1).
• The Emergency stop button should not be pressed (E = 0, since the button is normally closed).
• Either there should be no object at the end (O = 0) or an overload detected (L = 1).
Based on the given case, answer the following questions:
1. Write the Boolean expression for motor M.
2. Create the truth table.
3. Draw the logic circuit.

Propositional Logic, Hardware Implementation, Arithmetic Operations 93