A greenhouse fan is controlled by three binary inputs. T is 1 when the temperature is above a preset value. W is 1 when a roof window is open. M is 1 when a...
Question 1 Report
A greenhouse fan is controlled by three binary inputs. T is 1 when the temperature is above a preset value. W is 1 when a roof window is open. M is 1 when a gardener uses the manual fan switch. The output F is 1 when the fan is running.
The intended control rule is: the fan runs automatically when the temperature is high and the roof window is not open. The gardener can also run the fan using the manual switch, regardless of the values of T and W. The Boolean expression is represented by the incomplete statement below.
F = (T ___ NOT W) ___ M
(a) State what F = 0 means. [1]
(b) Give the value of F when T = 0, W = 1 and M = 1. [1]
(c) Complete the Boolean expression using the correct operators. [2]
(d) State the value of F when T = 1, W = 0 and M = 0. [1]
(e) Identify the Boolean operator that is evaluated first in the expression inside the brackets. [1]
(f) Convert the expression into a sequence of logic gates, stating the gate used for each operation. [2]
(g) Explain how the expression ensures that the manual switch overrides the automatic control. [2]
(h) Give one combination of T, W and M for which the fan is off. [1]
(i) Give the simplest expression for F when M is permanently set to 0. [2]
Answer Details
(a) \(F=0\) means the fan is not running [1].
(b) With M = 1, the manual control makes the final OR result 1 [1].
(c) \[F=(T\text{ AND NOT }W)\text{ OR }M\] [2]
(d) For T = 1, W = 0, M = 0: NOT W = 1, so \((1\text{ AND }1)\text{ OR }0=\textbf{1}\) [1].
(e) The NOT operation is evaluated first inside the brackets [1].
(f) Pass W through a NOT gate; input T and NOT W into an AND gate; input that AND output and M into an OR gate [2].
(g) M is an input to the final OR gate. When \(M=1\), the OR output is 1 regardless of the automatic-control result, so manual control overrides it [2].
(h) One off combination is T = 0, W = 0, M = 0 [1].
(i) If M is permanently 0, \[F=(T\text{ AND NOT }W)\text{ OR }0=T\text{ AND NOT }W\] [2].
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