# Combinational Logic Circuit

A Heater and a thermometer with four sensors:

a, b, c, d (input variables) ((a = highest temperature to d = lowest temperature))

Particular sensors indicate logical 1, if temperature is above level Ta, Tb, Tc , Td.

Design a circuit for three switches: Sw1, Sw2 and Sw3, Sw4 (outputs) so that the heaters can operate in series or in parallel connection.

(1) The temperature < Td --- H1 and H2 work in parallel
(2) Td < the temperature < Tc --- only H1 is working
(3) Tc < the temperature < Tb --- only H2 is working
(4) Tb < Temperature < Ta -- H1 and H2 work in series
(5) T ≥ Ta --- H1 and H2 are NOT working

I was just wondering if someone could give me some feedback. I've made a truth table with the input variables (temperature) and with the output variables (sensors) below.

Ta | Tb | Tc | Td |
0 | 0 | 0 | 0
0 | 0 | 0 | 1
0 | 0 | 1 | 0
0 | 0 | 1 | 1
0 | 1 | 0 | 0
0 | 1 | 0 | 1
0 | 1 | 1 | 0
0 | 1 | 1 | 1
1 | 0 | 0 | 0
1 | 0 | 0 | 1
1 | 0 | 1 | 0
1 | 0 | 1 | 1
1 | 1 | 0 | 0
1 | 1 | 0 | 1
1 | 1 | 1 | 0
1 | 1 | 1 | 1

Sw1 (A) | Sw2 (B) | Sw3 (C) | Sw4 (D) | OUTPUT
0 | 0 | 0 | 0 | 0
0 | 0 | 0 | 1 | 0
0 | 0 | 1 | 0 | 0
0 | 0 | 1 | 1 | 1 (5)
0 | 1 | 0 | 0 | 1 (3)
0 | 1 | 0 | 1 | 1 ***
0 | 1 | 1 | 1 | 1 ***
1 | 0 | 0 | 0 | 0
1 | 0 | 0 | 1 | 1 (2)
1 | 0 | 1 | 0 | 0
1 | 0 | 1 | 1 | 1 ***
1 | 1 | 0 | 0 | 1 ***
1 | 1 | 0 | 1 | 1 (1)
1 | 1 | 1 | 0 | 1 (4)
1 | 1 | 1 | 1 | 1 ***

*** I'm not sure if these outputs should be 1's or X (don't care states) on the truth table. I've attached a photo of the circuit.

Y= CD + B + BD + BCD + AD + ACD + AB + ABD + ABC + ABCD

Y = CD + AD + B (reduced form)

Therefore the circuit is:

C
-----AND GATE -----------
D

A
-----AND GATE --------- (3 INPUT OR GATE (CD, AD and B all lead to this OR gate)
D

B -------------------------

Sw1 (A) Sw2 (B) Sw3 (C) Sw4 (D) OUTPUT
0 1 1 0 1

According to the reduced function, if Sw2 (B) is on 1 then the output will always be 1. However, this appears to contradict the photo in which Sw2 (B) relies upon Sw3 (C) being 0 so that the circuit can loop around and have an output of 1.

I think I've overthought this a little bit so I might just leave it here for now and see if anyone can give me some feedback. Cheers!

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256bits
Gold Member
Hello says

Temperature sensor truth table:
Does the problem state a particular sensor will send a signal above a threshold temperature?
Is that sensor signal dependent upon what another sensor is sending?

Design a circuit for three switches: Sw1, Sw2 and Sw3, Sw4 (outputs) so that the heaters can operate in series or in parallel connection.
I see 4 switches.
I also see 4 in the truth table and in your picture post.

Maybe you could clarify more clearly.

From the circuit: It does seem to be problematic.
If the switch 3 is between the bottom connection of heaters 1 and 2 and the bottom rail, then switch 3 would be closed for the heaters to operate either singly or in parallel.
There would then appear to be no series circuit.

If the switch 3 is along the bottom rail, then the heaters can operate in series, or not at all.
Not sure where the bottom connection of the two heaters fits to which side of switch 3.

Yes, the whole question is a bit confusing in my opinion -- especially the "design a circuit with 3 switches, sw1, sw2, sw3, sw4" bit...

I think they mean to design a circuit with 4 switches, and it was just a typing error! I'm just going to design a circuit with 4 switches.

I've attached a new photo with some new calculations.

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If the temperature is above a certain level, then do all the other temperature sensors below it also have to be a logic 1?

For example: Ta | Tb | Tc | Td OUTPUT: sw1 = ? sw2 = ? sw3 = ? sw4 = ?
1 0 0 0

In my mind this isn't possible, because the temperature cannot be above Ta but below Tb, Tc, and Td. In this case I would take the output value from the previous row on the truth table and insert that into the output:

Ta | Tb | Tc | Td OUTPUT: H1 and H2 work in series
0 1 1 1 sw1 = 1 sw2 = 1 sw3 = 1 sw4 = 0

Therefore:

Ta | Tb | Tc | Td OUTPUT: sw1 = 1 sw2 = 1 sw3 = 1 sw4 = 0
1 0 0 0

P.S. Formatting! Sorry.

256bits
Gold Member

Yes, the whole question is a bit confusing in my opinion -- especially the "design a circuit with 3 switches, sw1, sw2, sw3, sw4" bit...

I think they mean to design a circuit with 4 switches, and it was just a typing error! I'm just going to design a circuit with 4 switches.

I've attached a new photo with some new calculations.
A typo could be possible, I wasn't sure if I was not reading it correctly.
I do think it is possible to have a circuit with 3 switches and operate as they state.

Code:
Truth table ** would be:    dc=don't care

Switch                  Heater
1     2     3          1     2        Comments
Off  Off   Off        Off   Off    All heaters off
On   Off   Off        On    Off    Heater 1 On
Off  On    Off(*)     Off   On     Heater 2 On
On   On    Off        On    On     Parallel
Off  Off   On         On    On     Series
* Circuit would still function with a 'dc', but best for an Off for optimization, safety, failsafe.
** another mirror circuit could be made, except connections for Switch 3 and Switch 2 have to be changed.

256bits
Gold Member
P.S. Formatting! Sorry.
No problem.
You can format in the code window, by selecting the + symbol in the menu, and type away in the pop up window.

A typo could be possible, I wasn't sure if I was not reading it correctly.
I do think it is possible to have a circuit with 3 switches and operate as they state.

Code:
Truth table ** would be:    dc=don't care

Switch                  Heater
1     2     3          1     2        Comments
Off  Off   Off        Off   Off    All heaters off
On   Off   Off        On    Off    Heater 1 On
Off  On    Off(*)     Off   On     Heater 2 On
On   On    Off        On    On     Parallel
Off  Off   On         On    On     Series
So this truth table corresponds to:

ROW 1: T ≥ Ta --- H1 and H2 are NOT working
ROW 2: Td < the temperature < Tc --- only H1 is working
ROW 3: Tc < the temperature < Tb --- only H2 is working
ROW 4 The temperature < Td --- H1 and H2 work in parallel
ROW 5: Tb < Temperature < Ta -- H1 and H2 work in series

I'm trying to understand what this circuit will look like now. What the function will be and what gates it will have.

I think I have to draw a diagram of the circuit as well and write down the function, but I'm a little confused because there is a H1 and H2 output.

H1 = sw1 NOTsw2 NOTsw3 + sw1 sw2 NOTsw3 + NOTsw1 NOTsw2 sw3
H2 = NOTsw1 sw2 NOTsw3 + sw1 sw2 NOTsw3 + NOTsw1 NOTsw2 sw3

H1 & H2 BOTH WORKING: sw1 sw2 NOTsw3 + NOTsw1 NOTsw2 sw3

I think I might assign letters to each of the switches and then try to derive a simpler expression. I don't think I need the H1 & H2 both working function either.

H1 = A 'B 'C + A B 'C + 'A 'B C
H2 = 'A B 'C + A B 'C + 'A 'B C

Both of these functions don't make sense. :s

256bits
Gold Member
H1 = A 'B 'C + A B 'C + 'A 'B C
H2 = 'A B 'C + A B 'C + 'A 'B C

Both of these functions don't make sense. :s
I really feel for you on this. I do absolutely dislike truth tables and trying to make a circuit from them.

I don't know if I should give you the circuit I came up with as it might be cheating, but here goes anyways.
Hopefully this is correct to work.

1. Draw the top rail V and the bottom rail Grd
2. Put 2 heater resistors upright to the rails but do not connect to the rails. Label H1 to the left, H2 to the right.
3. Connect H1 to the top rail.
4 Connect H2 to the top rail.
5 erase the top rail connection between H1 and H2.
6. Put a swithch in there. Label S2
7 Put a switch S1 between H1 and the bottom rail.
8 Connect H2 to the bottom rail
9. Locate the bottom of H1 before S1 and the top of H2. connect these 2 positions with switch S3.

( You can change the locations of S1, S2, S3 and H1, H2 if preferrred, with corresponding thruth table changes.
You might want to do that anyways to see how the truth tables differ )

Now with all switches open, no current can flow and all heaters off.
By a selection of switches open and closed, H1 and H2 can operate as needed.
Note that with all switches closed, there is a short circuit.
Hopefully I did not make an error.

What you should do is expand the switch and heater table for all 8 occurances of switches open/closed and heaters On/Off.
Easier to see what is going on.
Some might be Don't Care, or Dissallowed states of switches.
( some of the Don't Cares might be converted to Dissallowed in real life, sometimes it is not necessary to do so )

The big part is now doing the AND/OR gates for this to function, and tying in the temperature sensors.

PS I apologize for the late reply.

Another PS : For future consideration. You might want to consider posting in the Homework Section as it gets replies like toute de suite.

V-----------SWITCH2------H2--------
|
|
|
|
--H1------SWITCH1--------------GRND

Like this? I would have put switch three above GRND and connected it on the right hand side of the circuit but formatting... hahaha

Actually, I'm trying to see how the circuit would work in series now I take a second look...

This circuit looks a bit better.

EDIT: H2 should be to the left hand side of switch 2, then I think everything is fine.

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Ok, this is my final answer. I think everything looks good now. Thank you very much for your feedback 256bits! :D

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256bits
Gold Member
Ok, this is my final answer. I think everything looks good now. Thank you very much for your feedback 256bits! :D
Super.
I guess we really didn't cheat, cuz your circuit is different than mine, and it seems to work.

cheers