Digital logic design problem

[goldriver]

n an industrial unit four motors M1, M2, M3 & M4 are in operation .The system in
Figure below consists of four manual on/off switches S1, S2 , S3 & S4 (to turn on /off
motors respectively) And control logic and motor drive interface. Design a control logic
that performs the following operation
• All motor are not allowed to work at the same time.
• Motors M1, M2, M3 are allowed to work at the same time.
• Motors M2 & M4 cannot be operated at the same time.
• Single motor can be operated.
• Motors M3 & M4 cannot be operated at the same time.
• Motors M1 & M4 can work at the same time.
• Consider all other cases don’t care except the above.
• Remember that the controller must shut down all motors for the conditions that
are not allowed.
Please draw or write
1. Truth Table
2. Circuit Diagram
3. Optimal Circuit
4. Problem you faced

how to figure out the relationship between the inputs and outputs?

[Thomas W]

1. Truth table:
First I fill in the conditions from the list:
[code] | S1 | S2 | S3 | S4 | M1 | M2 | M3 | M4 |
0 | 0 | 0 | 0 | 0 | | | | |
1 | 0 | 0 | 0 | 1 | | | | 1 |
2 | 0 | 0 | 1 | 0 | | | 1 | |
3 | 0 | 0 | 1 | 1 | | | 0 | 0 |
4 | 0 | 1 | 0 | 0 | | 1 | | |
5 | 0 | 1 | 0 | 1 | | 0 | | 0 |
6 | 0 | 1 | 1 | 0 | | | | |
7 | 0 | 1 | 1 | 1 | | 0 | 0 | 0 |
8 | 1 | 0 | 0 | 0 | 1 | | | |
9 | 1 | 0 | 0 | 1 | 1 | | | 1 |
10 | 1 | 0 | 1 | 0 | | | | |
11 | 1 | 0 | 1 | 1 | | | 0 | 0 |
12 | 1 | 1 | 0 | 0 | | | | |
13 | 1 | 1 | 0 | 1 | | 0 | | 0 |
14 | 1 | 1 | 1 | 0 | 1 | 1 | 1 | 0 |
15 | 1 | 1 | 1 | 1 | 0 | 0 | 0 | 0 |[/code]
Note: In case 3, for example, you could choose to turn on ONE of the motors.

Then I fill out the empty cells to make sure the state of each motor matches the state of the corresponding input switch:
[code] | S1 | S2 | S3 | S4 | M1 | M2 | M3 | M4 |
0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
1 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 1 |
2 | 0 | 0 | 1 | 0 | 0 | 0 | 1 | 0 |
3 | 0 | 0 | 1 | 1 | 0 | 0 | 0 | 0 |
4 | 0 | 1 | 0 | 0 | 0 | 1 | 0 | 0 |
5 | 0 | 1 | 0 | 1 | 0 | 0 | 0 | 0 |
6 | 0 | 1 | 1 | 0 | 0 | 1 | 1 | 0 |
7 | 0 | 1 | 1 | 1 | 0 | 0 | 0 | 0 |
8 | 1 | 0 | 0 | 0 | 1 | 0 | 0 | 0 |
9 | 1 | 0 | 0 | 1 | 1 | 0 | 0 | 1 |
10 | 1 | 0 | 1 | 0 | 1 | 0 | 1 | 0 |
11 | 1 | 0 | 1 | 1 | 1 | 0 | 0 | 0 |
12 | 1 | 1 | 0 | 0 | 1 | 1 | 0 | 0 |
13 | 1 | 1 | 0 | 1 | 1 | 0 | 0 | 0 |
14 | 1 | 1 | 1 | 0 | 1 | 1 | 1 | 0 |
15 | 1 | 1 | 1 | 1 | 0 | 0 | 0 | 0 |[/code]
Next I convert the truth table for each motor to a Karnaugh map. This is for M1:
[code]M1 S1 S2
| 00 | 01 | 11 | 10 |
| 00 | 0 | 0 | 1 | 1 |
S3 S4 | 01 | 0 | 0 | 1 | 1 |
| 11 | 0 | 0 | 0 | 1 |
| 10 | 0 | 0 | 1 | 1 |[/code]

The map has 3 groups in it:

[code]M1 = S1 S2' + S1 S3' + S1 S3 S4'[/code]

' <-- means NOT = inverted.
+ means OR-gate.
S1 S2' means that the two factors should be multiplied (* <-- not shown). Multiplication = * = AND-gate.

(Repeat for M2, M3 and M4).

2. Circuit diagram: (from TKGate 1.8.7 on Ubuntu 11.04)
[img]http://diagramtips.com/images/2011/m1_logic_circuit.jpg[/img]

(Repeat for M2, M3 and M4).

3. ?

4. Problems: I can't install kmm (karnaugh map minimizer) on Ubuntu 11.04 :
[code]./kmm: error while loading shared libraries: libwx_gtk2_xrc-2.6.so.0: cannot open shared object file: No such file or directory[/code]