To detect a fire in a room, 3 (three) smoke detectors are used. If only one detector is active, the fire alarm remains inactive. The new alarm becomes active when two or three detectors become active. Derive the logical function of the alarm. In this work you can apply 'positive logic'. Perform the following steps. a) Compile the Truth Table of the Alarm function. b) Give the logical function of the Alarm in the canonical form of the SoP. c) Give the logical function of the Alarm in canonical form of PoS. d) Simplify the canonical function SoP according to the results of item (b) by using boolean algebra. (hint: modify/insert Theorem T1, a + a = a, on certain terms of the equation, then simplify)

Electricity for Refrigeration, Heating, and Air Conditioning (MindTap Course List)
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Chapter9: Components For Electric Motors
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To detect a fire in a room, 3 (three) smoke detectors are used. If only one detector is active, the fire alarm remains inactive. The new alarm becomes active when two or three detectors become active.

Derive the logical function of the alarm. In this work you can apply 'positive logic'. Perform the following steps.

a) Compile the Truth Table of the Alarm function.

b) Give the logical function of the Alarm in the canonical form of the SoP.

c) Give the logical function of the Alarm in canonical form of PoS.

d) Simplify the canonical function SoP according to the results of item (b) by using boolean algebra.

(hint: modify/insert Theorem T1, a + a = a, on certain terms of the equation, then simplify)

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