# truth table to digital logic gate

#### denison

Joined Oct 13, 2018
283
the truth table is A B OUT
1 1 0
0 1 1
0 0 1
1 0 0
I cannot find a digital logic gate that gives the truth table result.
There are very good online calculators for complex mathematical equation solving but I cannot find one for converting a truth table to the necessary digital logic gates. Does anyone know of such an online calculator?
Can the forum give me a digital logic gate for the above truth table or combination of logic gates?

#### sc0tch

Joined Nov 6, 2018
64
That is simply inverting A and not evaluating B. So just a simple single input inverter gate.

#### crutschow

Joined Mar 14, 2008
29,466
Are you sure that truth table is correct?

#### denison

Joined Oct 13, 2018
283
That is simply inverting A and not evaluating B. So just a simple single input inverter gate.
thanks scotch. didn't see that.

#### sc0tch

Joined Nov 6, 2018
64
thanks scotch. didn't see that.
No problem. Remember any truth table for 2 inputs should be expressible as And, Or, Nand, Nor, X-Or, X-Nor. Then for single input gates you can either Buffer or Invert

#### denison

Joined Oct 13, 2018
283
Are you sure that truth table is correct?
my post printed out wrong . the headings were moved to the right. they are correct when I try to edit so I can't fix it. scotch could see that and has provided the logic gate I need.

#### WBahn

Joined Mar 31, 2012
26,398
No problem. Remember any truth table for 2 inputs should be expressible as And, Or, Nand, Nor, X-Or, X-Nor. Then for single input gates you can either Buffer or Invert
If you are saying that any 2-input truth table is one of those six functions, then that is not correct. Those are merely six of the sixteen possible functions. More specifically, they are the six non-trivial symmetric functions. There are also two trivial symmetric functions, namely HI and LO. Then there are the four functions that degenerate into the 1-input functions, namely A, A', B, and B'. But that leaves the four non-trivial, non-symmetric functions. For instance

A B Y
0 0 1
0 1 1
1 0 0
1 1 1

#### sc0tch

Joined Nov 6, 2018
64
If you are saying that any 2-input truth table is one of those six functions, then that is not correct. Those are merely six of the sixteen possible functions. More specifically, they are the six non-trivial symmetric functions. There are also two trivial symmetric functions, namely HI and LO. Then there are the four functions that degenerate into the 1-input functions, namely A, A', B, and B'. But that leaves the four non-trivial, non-symmetric functions. For instance

A B Y
0 0 1
0 1 1
1 0 0
1 1 1
My apologies WBahn. Those were the only ones we covered in my degree program, along with the single input gates. And of course learned to be able to build any truth table using combinations of these gates.

Such as I would express the above as OR(A',B)

Last edited:

#### WBahn

Joined Mar 31, 2012
26,398
My apologies WBahn. Those were the only ones we covered in my degree program, along with the single input gates. And of course learned to be able to build any truth table using combinations of these gates.

Such as I would express the above as OR(A',B)
No apologies needed. I don't think any of the four non-degenerate non-symmetric gates are covered in any of the many textbooks I have and I don't think there has ever been an SSI implementation of any of them, either (though they are occasionally implemented as basic gates within ICs when they are useful enough). I'm pretty sure I had a prof that mentioned them in passing, but it wasn't until years later that I looked into it more in depth.

Interestingly, many texts claim that NAND and NOR are the only two "universal gates", meaning that any Boolean logic function could be implemented with nothing but a sufficient supply of either one of them. This tells me that the authors of these texts have also not looked beyond what they were taught (and thereby not realizing that an engineering degree is really little more than a license to go out and learn so much more). The logic table I provided is for the "material implication" gate and it is universal, as are the other three.

#### sc0tch

Joined Nov 6, 2018
64
No apologies needed. I don't think any of the four non-degenerate non-symmetric gates are covered in any of the many textbooks I have and I don't think there has ever been an SSI implementation of any of them, either (though they are occasionally implemented as basic gates within ICs when they are useful enough). I'm pretty sure I had a prof that mentioned them in passing, but it wasn't until years later that I looked into it more in depth.

Interestingly, many texts claim that NAND and NOR are the only two "universal gates", meaning that any Boolean logic function could be implemented with nothing but a sufficient supply of either one of them. This tells me that the authors of these texts have also not looked beyond what they were taught (and thereby not realizing that an engineering degree is really little more than a license to go out and learn so much more). The logic table I provided is for the "material implication" gate and it is universal, as are the other three.
Yeah my textbooks have every gate broken down to NOR and NAND gates for all gates other than AND and OR. And this is why I enjoy this forum so much. Everybody here always seems to have unique perspectives generated from their experience. For any question there is rarely one definitive academic answer but instead many different answers and approaches with various pros and cons but all(or at least most) technically correct.