Well in the version you pasted, you seem to be missing an end somewhere...  I couldn't really test anything but the logic (which is fine like you said) without knowing where it goes

Well, after adding a couple simple things you missed (don't know if it was just in the pastebin or what) and changing the output format a bit, and removing a lot of excess parenthesis, it seems to work fine:
:ClrHome
:Delvar L132->Dim(L1
:1->P :1->O
:24->M
:For(N,0,1
:0->L:1->I
:While L<M
:Repeat A
:getkey->B
:(B=92)+(B=102->A
:(B=92->L1(P+L
:End
:Output(N,I,Ans
:I+1->I
:L+8->L
:End
:End
:ClrHome
:For(N,0,2
:L1(P) xor L1(P+1->L1(P+3
:L1(P+3) xor L1(P+2->L1(P+6
:L1(P+2) and L1(P+3->L1(P+4
:L1(P) and L1(P+1->L1(P+5
:L1(P+4) or L1(P+5->L1(P+8
:Output(N+1,1,L1(P+6
:Output(N+1,3,Ans
:1+O->O
:P+8->P
:End
You do realize that it's reading the bits --> that way, not <-- like normal, right?...

It's a simulation of how electronics internally add numbers

Cooliojazz:eh it still is not working for me (it runs but does not give correct output), also i didn't think about the order at the time of programming, i suppose that would make the resulting output backwards wouldn't it? (If you mean what i think you mean) that shouldn't affect the result other than reading order though right?

ah, i see now. I think that is why the output is wrong too then, it looks like it is right but just messed up because of that ordering, i will switch that quick and see if it gives the output i originally expected heh

okay i found some small errors and tweaked a few things internally and now it works, i am going to change the input and output methods and then i will post the working source in case anyone is interested
also if you are wondering why i was working on a full adder in ti-basic, its because i am planning a little virtual-calculator-on-a-calculator
I started with a flip-flop and then a 1-bit full adder, now the 3-bit full adder, my next plan is to increase the size of this full adder to probably 1 byte, and then i will make it into a signed adder/subtractor

increased the adder size to a nibble and finished the i/o stuffs i will post the source in a sec if anyone wants to see next i will be changing it into an adder/subtractor

Edit: heres the source

:ClrHome
:1->O
:Lbl 1
:Delvar MDelvar L131->dim(L1
:1->P
:1->I
:28->L
:For(N,0,1
:While L>M
:Repeat A
:getkey->B
:(B=92)+(B=102->A
:(B=92->L1(P+L-7
:End
:Output(O,I,Ans
:I+1->I
:L-7->L
:End
:29->L
:M+1->M
:Output(O,I,"+
:I+1->I
:End
:Output(O,I-1,"=
:For(N,0,3
:L1(P) xor L1(P+1->L1(P+3
:Ans xor L1(P+2->L1(P+6
:L1(P+2) and L1(P+3->L1(P+4
:L1(P) and L1(P+1->L1(P+5
:Ans or L1(P+4->L1(P+9
:P+7->P
:End
:28->L
:For(I,11,14
:Output(O,I,L1(L
:L-7->L
:End
:O+1->O
:Goto 1
also to be clear, that delvar line is
:Delvar M
:Delvar L1
:31->dim(L1
not
:Delvar M
:Delvar L
:131->dim(L1