It does amaze me at this point you can just look at these circuits and figure out what is going on, that is a VERY cool thing to be able to do.

It comes from a LOT of practice and a LOT of work developing an intuitive feel for the fundamentals. For instance, as soon as I saw your second problem, I immediately applied DeMorgan's theorem in my had and knew what the equivalent basic gate was. But, even with a quarter century of experience, I wasn't able to quickly figure out the first circuit by just looking at it. I probably could have given more time than I was willing to spend on it, but when the answer didn't come quickly, I pulled out a pen and snagged a nearby envelope and walked through the truth table step by step.

One thing you definitely do need to do is internalize the basic logic gates. You need to be able to draw the truth tables or determine the outputs for a given set of inputs for the 1 input gates (BUF and INV) and the symmetric two-input gates (AND, OR, XOR, NAND, NOR, XNOR). If you have to memorize them at first, then memorize them. But eventually you need to simply understand what each one means. If you understand INV, AND, OR, and XOR in terms of the fundamental everyday meanings, then you can figure out all the rest.

 

OK, thanks I finally got it, its OR and I'm 100% this time. I got it by watching a few youtube videos. But here is the BIG but, I REALLY want to understand truth tables, how to create them and how to read them. I'm sorry I was a pain in the butt student tonight. My instructor I'm sure feels the same way at times. Any websites or specific youtube videos that would really help me master truth tables? Oh an am I making this out to be harder that it really is? I often do that, I over think stuff sometimes. Thanks again for the help, and patience!

 

PF, the question remains as to why you won't post your attempts at the truth tables. Yes, I believe you are making out to be something that is much harder than it is, but we simply cannot help resolve that unless you give us something to work with.

 

OK, explain to me how to me how I'm created a truth table out of this? Based on my own logic here, and process of elimination its got to be an AND operation, no? Still explain to me how do I create a truth table here?

I always go left to right, starting at the inputs. Each time the input changes, I note it. I am able to do it mentally, but if you can't do that, write it down. It is a lot easier than you think it is. You just need to clear your mind and think logically (pun intended). Use scrap paper. Write on the circuit. I think you just think you can't do it, and you're blocking yourself from learning. Take it slow and easy, one step at a time. Identify specific problems that confuse you, and focus on them. Once you have the pieces, you can work on the full problem.

You have not been a "pain-in-the-butt student". You want to learn, and there's no shame in that. I think the only problem is that you need to learn how to learn--focus on individual problems rather than the problem as a whole. But no, you've done nothing wrong, and please don't feel like you have. All students are confused by something, and it's our job to clear it up

 

As for truth tables and how they work, let me see what I can do to help with that.

Let's start by explaining the inputs. Each input has a corresponding bit (either a 0 or a 1) that shows the state of the input.

1 input means there are two possible input combinations (2^1). These combinations are either 0 or 1.

2 inputs means there are 4 possible combinations (2^2). These combinations are 00, 01, 10, and 11, where each bit represents an input (A or B).

3 inputs means there are 8 possible combinations (2^3). These combinations are 000, 001, 010, 011, 100, 101, 110, and 111.

If you know binary, it will help a lot. If you look at those combinations, you'll see that they count from 0 to 7: 000=0, 001=1, 010=2, 011=3, 100=4, etc. That's just going to help you figure out the order to put them in.

Now, the first thing to do when you need to set up a truth table is determine how many inputs you have. Draw a 'T' chart with the inputs on the left and the output on the right. The inputs are all going ot be in the same order which I described above--counting from 0 to one less than 2^(number of inputs). Again, each bit represents the state of an input.

Once it's set up, look at the input combinations (start with 000, for a 3-input) and look at the circuit. Pretend the inputs in the circuit are A=0, B=0, and C=0. Follow A first. Every time A changes, write it down on the wire right after it changes, so you can see what it is at that point in the circuit. Follow this until you get to the first AND or OR gate, then move on to B. Do the same thing until all the inputs have been traced. Then you can look at the inputs to the logic gates (AND and OR) and perform the operation. You'll need to do this for every gate in the circuit. When you're done, you should get one output. This is what you'll put in the "output" column of the truth table, across from 000, to show that it is the result for that combination.

Do this for all the other combinations, until the T chart is all filled in. The T chart is the truth table.

I know this explanation is very long and drawn-out, but the whole thing shouldn't take you more than 5 minutes to complete.

I hope this clears things up. I may try to make a video tutorial at some point, but I can't guarantee it. I've been very busy lately I'll see what I can do, though!

Best wishes,
Matt

 

Thanks for the big post. I'm going to work on truth tables after the next few exams, I only have 3 left to graduation. Then I'm gonna take my credits to a state college for my AAS degree in Electrical/mechanical systems and maintenance. Kinda in a bit different direction than ET. I'd like to work on industrial systems and machines. I have a LONG way to go. Finish this and then with credits already earned I probably will need roughly 24 more credits to get my degree.
Anyway if I need some help in the set of lessons, I know where to look. You guys have been INCREDIBLE! I can't begin to tell you how grateful and appreciative I am for your knowledge. I can't say it enough, thank you!