Hi everyone,
Is there a proper name to distinguish NAND-like universal modules from ordinary ones, that is, the ones formed by a function F, plus NOT, plus ONE, and ZERO?
Thanks, Candida
--- Candida Ferreira, Ph.D. Chief Scientist, Gepsoft
GEP: Mathematical Modeling by an Artificial Intelligence
Question doesn't make sense to me.
Try again or pick up a logic book.
Maybe you refer to fixed logic v tablelogic?
So what brings someone in your esteemed field down into the hw trenches.
johnjakson at usa dot com
NAND and NOR functions by themselves can be used to describe any other function, including NOT, ZERO and ONE. But, for instance, the 3-multiplexer, which is also by definition an ULM, can not by itself describe a NAND gate as it is unable to create a NOT gate. But there are other functions that behave exactly like NAND or NOR gates in the sense that, by themselves, they can also describe any other function. Do such functions have a name? I think there is something special about them and I would like to distinguish them from the ordinary ULMs.
Candida
--- Candida Ferreira, Ph.D. Chief Scientist, Gepsoft
GEP: Mathematical Modeling by an Artificial Intelligence
other
3-multiplexer,gate
that
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I think
them
I don't follow. Multiplexers are as complete as any logic element. I'm not sure what you mean by a 3-multiplexer, but I will assume you mean a 2 input mux with a single control input. You can get a NOT function by putting a 1 on the I0 input and a 0 on the I1 input and your signal on the sel input.
True. NCR once produced a computer using only NAND gates.
A four to one mux can make any boolean function of two variables. The mux selector takes the two inputs and the mux inputs become a function code.
A NAND or NOR is the simplest case, but requires multiple instances. A 4:1 mux is the simplest complete case for two inputs. There are cases in between and redundant cases, but those are not very interesting.
Not in digital electronics. Do some research on "Lattice Theory"
-- Mike Treseler
That's true and does not contradict the definition of a ULM, but you need the 1 and the 0 to create a NOT. Without them you cannot create a NOT with the 3-multiplexer. But there are other functions, such as the NAND and the NOR functions that, by themselves, can create any other function, without needing the NOT, the ZERO and the ONE. These are the ULMs I want to distinguish from the more ordinary ones.
Candida
--
Candida Ferreira, Ph.D.
Chief Scientist, Gepsoft
http://www.gene-expression-programming.com/author.asp
GEP: Mathematical Modeling by an Artificial Intelligence
http://www.gene-expression-programming.com/gep/Books/index.asp
Modeling Software
http://www.gepsoft.com/gepsoft/
Get APS 3.0 Std free with the book!
I've seen them named "complete logic gate set" or "primitive logic gate set". I am not sure whether there is a universally accepted name.
Do you mean, they are _generators_ for whole family of binary functions ?
MB
PS: there's a booklet by Emil Post on this subject of binary functions. Forgot the title, sorry.
-- Michel BILLAUD billaud@labri.fr LABRI-Université Bordeaux I tel 05 4000 6922 / 05 5684 5792 351, cours de la Libération http://www.labri.fr/~billaud 33405 Talence (FRANCE)
Yes, exactly like NAND and NOR. Just to give another example, you can also do that with the function a'c'+b'c.
Candida
--- Candida Ferreira, Ph.D. Chief Scientist, Gepsoft
GEP: Mathematical Modeling by an Artificial Intelligence
Michel Billaud wrote:
need
with
the
without
other
It's a good bet that they didn't use any NAND gates to generate ones or zeroes! This sounds like a mathematician kind of question rather than engineering...
A rose by another name.
I read NOT, ZERO, and ONE as inverter, tied low, tied high.
-- Mike Treseler
you
need
with
and the
without
Why?
Someone needs to tell me how to create a one or zero using only NAND gates.
The only thing I can think of would be to use two gates in a loop. This will have two stable states, 1-0 and 0-1. The two free inputs will set the gates to the two states when taken low since any input at a zero will make the output of the gate a one. One of these free inputs is tied to its twin input to make an inverter. The other is tied to its own gate output. If the gate output is a one, it causes no action on the gate and is stable. If a zero, it will cause itself to become a one and be then be stable.
But this will only generate a stable output after some period of time. Not exactly my idea of a useful circuit.
any
at
no
time.
This is why I said the problem was mathematical and not engineering. A Boolian NAND gate performs a truth function on ones and zeroes only. This is not the same as a Verilog NAND gate which can take X or Z as well as 1 or 0 and produce X as well as 0 or 1.
The Boolian NAND also does not imply a time delay. So given such a gate with an unknown input "A", you can produce the inversion of the unknown input "A_BAR" (A NAND A), and then create 1 by NANDing "A" with "A_BAR" (A NAND A_BAR). Zero requires an additional inverter (1 NAND 1).
In the real world this would produce glitches whenever "A" changed state.
Not desperately needing it, but anyway:
x nand (x nand x) = x nand not(x) = 1 and then [x nand (x nand x)] nand [x nand (x nand x)] = 0
MB
-- Michel BILLAUD billaud@labri.fr LABRI-Université Bordeaux I tel 05 4000 6922 / 05 5684 5792 351, cours de la Libération http://www.labri.fr/~billaud 33405 Talence (FRANCE)
[nand]
In the real world, who needs to get 0 and 1 from whatever gate anyway ?
BTW, this reminds me of a funny paper on how to build a triple not circuit using only 2 not gates (and a number of and- and or- gates).
MB
>-- Michel BILLAUD billaud@labri.fr LABRI-Université Bordeaux I tel 05 4000 6922 / 05 5684 5792 351, cours de la Libération http://www.labri.fr/~billaud 33405 Talence (FRANCE)
Because with them you can find interesting solutions using just one kind of gate. I think that, if for nothing else, this might be fun. And if fpga technology allows people to use different kinds of gate such as the
3-multiplexer, why not use other complex modules? And if you know for sure the module you are using is a NAND-like module you can even relinquish the use of inverters and build circuits using just that gate.Candida
--
Candida Ferreira, Ph.D.
Chief Scientist, Gepsoft
http://www.gene-expression-programming.com/author.asp
GEP: Mathematical Modeling by an Artificial Intelligence
http://www.gene-expression-programming.com/gep/Books/index.asp
Modeling Software
http://www.gepsoft.com/gepsoft/
Get APS 3.0 Std free with the book!
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