There's something wrong with my 2-bit adder

Question

I made a 2-bit adder in Logisim Evolution and for some reason it gives the wrong output. I searched a ton of forum posts and all of them use the exact same design and they say it works.

Here's a truth table:

Answer 1

I think you have the correct schematic. I think you have the right table. I just think you are not reading your table, correctly.

Here's your circuit done up in Neemann's Digital program (free):

That's exactly the same schematic as you have (maybe slightly neater and better labeled.) That table on the right is automatically generated for me by the program. It's not hand-done. And you can see that the table looks like an exact match for yours.

And this is all correct.

The problem in your reading of the table happens because the input bits are mixed up somewhat. The bits of 2-bit word \$A\$ and the bits of 2-bit word \$B\$ are intermingled, as you can see.

Let me relabel the entire thing so that it is an exact match with your result. This means that the inputs and outputs will be just as badly labeled, but the circuit otherwise unchanged:

Same thing you have. And it is right. Just terrible labels.

Now, let me -- once again -- re-order the table a bit. I'm going to use my nice labels, again. (Can't stand yours.) The only difference now will be that the table inputs are re-arranged. That's the only difference:

Now that's probably a little more readable. \$A\$ is arranged with its high-order bit on the left. Same with \$B\$. But now all of \$A\$ is together and all of \$B\$ is together. And I'm starting with \$0\$ for \$A\$ and walking through all of the values for \$B\$ first, before adding 1 to \$A\$ and repeating. So the table reads better now.

That's all there was. You are just fine.

You need to learn how to interpret what you see. That's all. Computers and simulators are just software. They don't know what to present to help you think and they certainly have no idea what you are expecting to see. They just do their work, generate stuff, and leave it to you to figure out the meaning.

Maybe someday in the future, AI-software will know what you want to see as a human and present exactly what you expect to see. But we aren't there, quite yet. So you still have to engage your brain. Oh, well. ;)

A last note. Neemann's Digital program has nice menu options:

See those nice things circled in blue? That allows me to choose the ordering for the tables I generated for you, above. Those very nice options make it really easy to generate tables with a desired ordering in their analysis. Trivial, in fact. I recommend the tool to you.