Verify Truth Table: Switches and LED

Question

I got a digital design problem. My final implementation of the circuit program didn't achieve the required criteria, so I brought my problem and my works here to be suggested by you if I mis-manipulated any details.

Logic System: Binary--1,0.

Issue after Simulation and Test on Circuit Board: LED lighted up at the begining without any switches were turned ON. (Would it make sense?)

Problem Statement:

Use 4 switches A, B, C, D to control a LED. LED is ON if the following conditions are satisfied,

D and B turn ON,

or A turns OFF while C turns ON,

or A and B turn ON and the rest turn OFF,

or C and D turn OFF,

or all switches turn ON.

End of Problem Statement.

Notations and Circuit Combinations we use:

AND gate: · (dot)

OR gate: +

"Not/Invert something": ~

SOP: Sum of Products

POS: Product of Sums

SOP and POS are equivilant to each other.

My works:

True Table based on the 5 criteria

ON:1, OFF:0.

Collection of LED results is {1011111110001101}.

I can handle operating the software part, but I really want to check with you guys if I use POS method and based on the 5 criteria given in the problem, whether or not my true table is correct.

Please help me to point out my blind spots. Thanks

Answer 1

Going by the problem definition directly:

1. D and B turn ON: B•D

2. A turns OFF while C turns ON: ~A•C

3. A and B turn ON and the rest turn OFF: This condition is already covered by condition 4.

4. C and D turn OFF: ~C•~D

5. all switches turn ON: This condition is already covered by 1.

So your final function is: B•D + ~A•C + ~C•~D

3 ands, 2 ors.