[SOLVED] Simplification truth table

[Carlos5Pierros]

Hi I am not sure about my result so I would like to ask you if you can correct me. the circuit is composed of a counter and its outputs enter a combinational logic block. And it is this block that I am trying to simplify.

counter | outputs Q
CBA | 1 2
-----------------
000 0 0
001 1 1
010 0 1
011 1 1
100 0 0
101 1 0

Q1 is simple is equal to output A
But Q2 is more complex look what I understand..

Q2 = /C * /B * A + /C * B * /A + /C * B * A

Simplified équation

Q2 = /C * A + /C * B

Thank for your time. I hope that is clear enough.

 

[KlausST]

Hi,

There are just 6 out of 8 rows. What's with the remaining two?

Klaus

 

[Carlos5Pierros]

Hi,

There are just 6 out of 8 rows. What's with the remaining two?

Klaus

Indeed I forgot to say that I will use a counter which I will clear at 0110. Does that answer your question?

 

[_Eduardo_]

Indeed I forgot to say that I will use a counter which I will clear at 0110.

Then you can write Q2 = /C * A + B

 

[d123]

Hi,

I'm not really seeing your formulas in those results, but that's just me.

Please post a schematic of the circuit described in post #1, please. It might help somewhat.

--- Updated Feb 19, 2021 ---

In my way of expressing it, I see:

Q1 = A + B(don't care) + C (don't care)
Q2 = !C + A OR B

Or, put differently:

Q1 = A + !B + !C OR A + B + !C OR A + !B + C
Q2 = A + !B + !C OR !A + B + !C OR A + B + !C

So:

Q1 = A, and Q2 = !C + A OR B

Is that what you mean?

--- Updated Feb 19, 2021 ---

Hi again,

This is my (clumsy) interpretation of one way of achieving the required goals with standard logic gates, as far as I have understood how you wish to implement it. Maybe there is a simpler solution, or maybe this is not how you need the inputs/outputs to be configured.

If I understood the functions correctly, Q1 = A can be a single in/single out path because B and C inputs are irrelevant (don't cares); Q2 = (!C + A OR B) needs to OR A and B inputs into an AND gate that only goes high in combination with !C (i.e. input C has to be low but inputs A and/or B must be high for Q2 to be high):

--- Updated Feb 19, 2021 ---

And hi, again,

Trying to think of a simpler solution/less parts, in principle, NOR gates seem a nice option. Same idea as previous schematics but only two quad packages and/or no (irritating) mixed logic and unused gates. You would need to check/think through that it really does fulfil the required functions - considered briefly, it seems to me it can. I'm sure there may be an even simpler solution.