Boolean Algebra Question

[N2TheRed]

I created a truth table with three inputs and randomly select high outputs so that I could practice doing boolean algebra. I've been able to answer some I've seen on the internet, but have failed when I just made up my own example to practice with. I've included a picture to see how far I got and ultimately where I've not been able to move past.

I have my rules cheat sheet beside me, but I'm going nowhere fast.

[barrym95838]

It has been about 30 years since I attempted any boolean algebra or Karnaugh mapping, so please take my limited advice with a grain of salt, but I think that you might be able to leave the first term alone and factor /C out of the second and third terms, ending up with /A/BC + /CA. Going back to your strategy, /AB + A/B can be reduced to A XOR B, but I don't know if introducing XOR into the mix is in line with what you are asking.

Mike B.

[N2TheRed]

barrym95838 wrote:

It has been about 30 years since I attempted any boolean algebra or Karnaugh mapping, so please take my limited advice with a grain of salt, but I think that you might be able to leave the first term alone and factor /C out of the second and third terms, ending up with /A/BC + /CA. Going back to your strategy, /AB + A/B can be reduced to A XOR B, but I don't know if introducing XOR into the mix is in line with what you are asking.

Mike B.

That's for the reply Mike.

I haven't tried what you mentioned yet, but I'm going to rework it as you suggested in the morning. However, I know of XOR, it's truth table and the gate symbol. When I went to reduce the term in the picture, I didn't immediately recognized that A~C + ~AC was an XOR until I plugged in a truth table. I was trying to factor out and reduce, but the example in the picture I fail to see what I'm missing. Does that mean you can go to factor out a term, but the resulting expression cannot be reduced? Given all the examples I've worked before, I just assume that every time you factor you can reduce. It doesn't appear so in that example.

[rwiker]

The way you should factor this is not via the first two terms, but the first and the third:

/A/BC + A/B/C + AB/C = A/B/C + AB/C + /A/BC = A/C(B+/B) + AB/C = A/C + AB/C

If you're going to practice doing this by hand, you should take a look at Karnaugh maps (e.g, https://en.wikipedia.org/wiki/Karnaugh_map)

[8BIT]

There is a minor error in this:

/A/BC + A/B/C + AB/C = A/B/C + AB/C + /A/BC = A/C(B+/B) + AB/C = A/C + AB/C

It should be:

/A/BC + A/B/C + AB/C = A/B/C + AB/C + /A/BC = A/C(B+/B) + AB/C = A/C + /A/BC

This truth table is a good example of logic that does not reduce to simple terms.

Daryl

[rwiker]

8BIT wrote:

There is a minor error in this:

/A/BC + A/B/C + AB/C = A/B/C + AB/C + /A/BC = A/C(B+/B) + AB/C = A/C + AB/C

If should be:

/A/BC + A/B/C + AB/C = A/B/C + AB/C + /A/BC = A/C(B+/B) + AB/C = A/C + /A/BC

Argh. Yes. It should be the same as the result that barrym got, and I thought I checked that... clearly not.

Quote:

This truth table is a good example of logic that does not reduce to simple terms.

Daryl

[dwight]

If you combine the bottom two terms, the B's cancel.
That is about the most I see.
The problems you may find are often like the math problems you get in grammar school.
You see problems like 24 / 3 but rarely 26 / 3.
Dwight

[N2TheRed]

Thanks for everyone that replied.

[N2TheRed]

rwiker wrote:

8BIT wrote:

There is a minor error in this:

/A/BC + A/B/C + AB/C = A/B/C + AB/C + /A/BC = A/C(B+/B) + AB/C = A/C + AB/C

If should be:

/A/BC + A/B/C + AB/C = A/B/C + AB/C + /A/BC = A/C(B+/B) + AB/C = A/C + /A/BC

What does the underline represent?

[N2TheRed]

8BIT wrote:

This truth table is a good example of logic that does not reduce to simple terms.

Daryl

If I'm understanding this correctly, I just happened to make up an example that was a little complex.

[8BIT]

N2TheRed wrote:

rwiker wrote:

8BIT wrote:

There is a minor error in this:

/A/BC + A/B/C + AB/C = A/B/C + AB/C + /A/BC = A/C(B+/B) + AB/C = A/C + AB/C

If should be:

/A/BC + A/B/C + AB/C = A/B/C + AB/C + /A/BC = A/C(B+/B) + AB/C = A/C + /A/BC

What does the underline represent?

it was the best way for me to point out what part was wrong... it has nothing to do with logic representation.

[8BIT]

N2TheRed wrote:

8BIT wrote:

This truth table is a good example of logic that does not reduce to simple terms.

Daryl

If I'm understanding this correctly, I just happened to make up an example that was a little complex.

Yes, sometimes you get lucky and your truth table will reduce to something simple...but more often than not (for me), I end up with something that is not much simpler than the original equation.

Daryl