Question

Exercise 8: The main stairway in a block of flats has three switches for controlling the lights. Switch A is located at the top of the stairs, switch B is located halfway up the stairs and switch C is positioned at the bottom of the stairs. Design a logic network to control the lights on the staircase.​

Answer 1

The logic network to control the lights on the staircase; has been designed as seen below.

How to describe Computer Logic Gates?

The truth table for the required response of the question is;

SWITCH A        SWITCH B         SWITCH C            Y

0(OFF)               0(OFF)               0(OFF)               0(OFF)

0(OFF)               1(ON)                  1(ON)                 1(ON)

1(ON)                  0(OFF)               1(ON)                 1(ON)

1(ON)                  1(ON)                  0(OFF)              1(ON)

1(ON)                  1(ON)                  1(ON)                0(OFF)

The expression for the output Y in SOP form will be;

A ⊕ B ⊕ C = A⁻B⁻C + AB⁻C⁻ + A⁻BC⁻

That's the output expression for the XOR gate.

Thus, we can conclude that in the staircase wiring, higher output is obtained when two out of three of the inputs are different.

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