Here's a solar heating system representation.

• The sun shines out of an intense blue sky onto a solar collector.
• The solar collector heats up.
• Fans can be used to move the accumulated heat in the collector to a rock bin - to store heat - or to the house itself.
• Fan A can be used to move air through the solar collector.
• Fan B can be used to move air into the heated space (the house).

• When either fan is OFF, air cannot move through that fan.
• When both Fan A and Fan B are ON air moves through the collector directly into the house.
• When Fan B is ON and Fan A is OFF air moves from the rock bin into the heated space.
• When Fan A is ON and Fan B is OFF (heated) air moves from the collector to the rock bin.

• When the heated area needs heat the signal H becomes TRUE.  This signal is supplied by a temperature sensor that compares measured temperature to desired temperature.
• When the rock bin is warmer than the heated space - and can supply heat - a signal RH is TRUE.  The measurements from two temperature sensors is compared to generate this signal, and the same scheme is used for the two measurements below.
• When the collector is warmer than the heated space the signal CH is TRUE.
• When the collector is warmer than the rock bin the signal CR is TRUE.

• Generate a truth table for all functions.  Here is a blank truth table.  FA is TRUE when Fan A is ON, and FB is TRUE when Fan B is ON.
• First, we note that when there is no need for heat to the heated space (H = 0), and the collector is warmer than the rock bin (CR = 1) we should move heat from the collector to the rock bin.  To do that, turn FAN A ON and B OFF.  That allows us to fill in four parts of the truth table.

• However, there is one situation here that is thought-provoking.  If CR = 1 (Collector warmer than the Rock bin), and if RH = 1 (Rock bin warmer than the Heated space.), then it is clear that CH = 1 (Collecter warmer than the Heated space.)  There are places in the truth table where that is not the case, and when CH = 0 in that situation, it's something that can't happen.  Since it can't happen, we don't care what the function is for that case.  That gives us a new truth table with DON'T CAREs.  We'll add DON'T CAREs wherever that happens.

 

H	RH	CH	CR	FA	FB
0	0	0	0
0	0	0	1	1	0
0	0	1	0
0	0	1	1	1	0
0	1	0	0
0	1	0	1	X	X
0	1	1	0
0	1	1	1	1	0
1	0	0	0
1	0	0	1
1	0	1	0
1	0	1	1
1	1	0	0
1	1	0	1	X	X
1	1	1	0
1	1	1	1

• Actually, we can note that anytime heat is needed and either the Collector or Rock bin can supply it, we need to turn on Fan A.  When we don't need heat, Fan A is OFF.  And, if we need heat (H = 1) and nothing can supply heat we won't turn on Fan A.  Let's put that into the truth table.

 

H	RH	CH	CR	FA	FB
0	0	0	0	0
0	0	0	1	1	0
0	0	1	0	0
0	0	1	1	1	0
0	1	0	0	0
0	1	0	1	X	X
0	1	1	0	0
0	1	1	1	1	0
1	0	0	0	0
1	0	0	1	0
1	0	1	0	1
1	0	1	1	1
1	1	0	0	1
1	1	0	1	X	X
1	1	1	0	1
1	1	1	1	1

• Next, we note that we turn on Fan B when

• Determine the simplest sum-of-products form for both fan functions.
• Be careful.  There may be some Don't Care terms in the truth table.  Think about what conditions are possible carefully.
• Show the circuit.