Question

QUESTION 3 [14 Marks] Ms Reginalda would like to have an automated lighting system for her bedroom. She is a Geologist at Ministry of Mines and Energy, hence she does not even know what a NAND gate is, however she is very enthusiastic about new technologies and automation. She approached you to design a digital system for automating her bedroom lights. The digital system should have three sensor inputs as shown in Fig 3 Sensor A: to detect if it is sunny or dark outside her house. Sensor B: to detect if the room curtain is closed or open and Sensor C: to detect her presence in the room. Inputs Output Sensor A Sensor B Digital System Lights (L) Sensor C Fig 3: System Block Diagram The system activate the Lights UNLESS the following conditions arise She is not in the room (Sensor C =0). She is in the room (Sensor C=1), but the curtain is open (Sensor B=1) and it is sunny outside (Sensor A =1). (a) Derive the truth table for this system. [4] (b) Obtain the SOP expression for the system from the truth table. [2] (c) Reginalda has a limited budget. Using Karnaugh Map techniques, minimise the SOP expression in (b). [4] (d) Derive the equivalent POS expression from the Karnaugh Map. [2] (e) Using the expression from (c), draw the logic circuit using only NAND gates. [2]

          QUESTION 3 [14 Marks]
Ms Reginalda would like to have an automated lighting system for her bedroom. She is a Geologist at
Ministry of Mines and Energy, hence she does not even know what a NAND gate is, however she is
very enthusiastic about new technologies and automation.
She approached you to design a digital system for automating her bedroom lights. The digital system
should have three sensor inputs as shown in Fig 3
Sensor A: to detect if it is sunny or dark outside her house.
Sensor B: to detect if the room curtain is closed or open and
Sensor C: to detect her presence in the room.
Inputs
Output
Sensor A
Sensor B
Digital System
Lights (L)
Sensor C
Fig 3: System Block Diagram
The system activate the Lights UNLESS the following conditions arise
She is not in the room (Sensor C =0).
She is in the room (Sensor C=1), but the curtain is open (Sensor B=1) and it is sunny outside
(Sensor A =1).
(a) Derive the truth table for this system.
[4]
(b) Obtain the SOP expression for the system from the truth table.
[2]
(c) Reginalda has a limited budget. Using Karnaugh Map techniques, minimise the SOP expression
in (b).
[4]
(d) Derive the equivalent POS expression from the Karnaugh Map.
[2]
(e) Using the expression from (c), draw the logic circuit using only NAND gates.
[2]

QUESTION 3 [14 Marks]
Ms Reginalda would like to have an automated lighting system for her bedroom. She is a Geologist at
Ministry of Mines and Energy, hence she does not even know what a NAND gate is, however she is
very enthusiastic about new technologies and automation.
She approached you to design a digital system for automating her bedroom lights. The digital system
should have three sensor inputs as shown in Fig 3
Sensor A: to detect if it is sunny or dark outside her house.
Sensor B: to detect if the room curtain is closed or open and
Sensor C: to detect her presence in the room.
Inputs
Output
Sensor A
Sensor B
Digital System
Lights (L)
Sensor C
Fig 3: System Block Diagram
The system activate the Lights UNLESS the following conditions arise
She is not in the room (Sensor C =0).
She is in the room (Sensor C=1), but the curtain is open (Sensor B=1) and it is sunny outside
(Sensor A =1).
(a) Derive the truth table for this system.
[4]
(b) Obtain the SOP expression for the system from the truth table.
[2]
(c) Reginalda has a limited budget. Using Karnaugh Map techniques, minimise the SOP expression
in (b).
[4]
(d) Derive the equivalent POS expression from the Karnaugh Map.
[2]
(e) Using the expression from (c), draw the logic circuit using only NAND gates.
[2]

Added by Jennifer G.

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