1. Home
  2. Electronics Design
  3. building boolean gates

building boolean gates

Hi all,

I am trying to build the following two linear gates from basic boolean gates (XOR, NOT, AND, OR):

  1. Enable gate with the following truth table where u,s,e are the inputs and w is the output u s e w
0 0 0 0 0 0 1 0 0 1 0 1 0 1 1 0 1 0 0 0 1 0 1 1 1 1 0 1 1 1 1 1 Basically what the gate does is if e=0 then it outputs s and if e=1 then it outputs u.
  1. This time I have a gate with 4 inputs r,e,s,t and two outputs c and c' The outputs are computed as follows: if e=1 then c=r XOR t and c' = NOT(r XOR t) if e=0 then c=c'=s

The first gate should not use any non-linear operation (i.e. not AND and OR) together with the u signal and the second gadget should not involve t in a non-linear operation. Both gadgets look pretty linear to me, so I hope this is somehow possible.

How can I "implement" these gadgets?

Regards and thanks a lot, Bernd

Reply to
Bernd Schneider
Loading thread data ...

Should be possible with XOR, NOT, AND and OR. But why not using just one chip like

formatting link
?

Two

formatting link 

--
Frank Buss, fb@frank-buss.de
http://www.frank-buss.de, http://www.it4-systems.de
Reply to
Frank Buss

Have you seen "And Or Select" gates? This is what they do.

formatting link

Again, the And Or Select form with the addition of a Not Xor gate pair looks pretty good.

--
Regards,

John Popelish
Reply to
John Popelish

Hi Frank,

I am sure that you can implement it with using only XOR, NOT, AND and OR but more intersting for me is whether you can actually implement it such that in the first case u and in the second case t is not involved in any non-linear operation.

Do you know of a way?

Regards, Bernd

Frank Buss wrote in news:1uj8z6uqrv57k.1qmupuqvcmi0t$. snipped-for-privacy@40tude.net:

Reply to
Bernd Schneider

I'm not an electronics specialist, what is a non-linear gate or operation?

--
Frank Buss, fb@frank-buss.de
http://www.frank-buss.de, http://www.it4-systems.de
Reply to
Frank Buss

Frank Buss wrote in news: snipped-for-privacy@40tude.net:

Non-linear gates are AND and OR gates. Linear gates are XOR and NOT.

Reply to
Bernd Schneider

John Popelish wrote in news:VaqdnSYOldRsohfVnZ2dnUVZ snipped-for-privacy@comcast.com:

This gate however uses AND gates. I am not sure though it one of the AND or OR gates in the figure gets as input the u bit. Maybe you can help me to figure out this issue.

Regards and thanks, Bernd

Reply to
Bernd Schneider

There are some program's that will take as input a truth table and output circuit's that express table.

One I like very much is "logic friday". It lets you select the gates you want and even gives you a circuit(that isn't necessarily perfect but close).

Reply to
Jon Slaughter

The question isn't how, it's why?

John

Reply to
John Larkin

John Larkin wrote in news: snipped-for-privacy@4ax.com:

I put implement in "" because probably in practice nobody will ever implement it. It is only a theoretical experiment.

I figured out that my first gadget is a multiplexer and that I can implement it with two and gates and one or gate, i.e. w = (s AND NOT(e)) OR (u AND e). Now, my question is: can I also implement it without the AND gates? Note that u and s should not be input to a non-linear gate. Somewhat this multiplexer construction looks similar to a XOR gate itself. I wonder whether there is a way to implement it with a XOR gate.

Regards, Bernd

Reply to
Bernd Schneider

I see. This sounds a bit like reversible gates, which I've read about some time ago, related to cellular automata. E.g. the Fredkin gate (I've just added a logic function with XOR and AND gates to the Wikipedia entry for this gate)

formatting link

This is a reversible universal gate (and mass conserving, if you would really implement it with billiard balls), with which you can implement your function. The XOR gate alone is not an universal gate (see

formatting link
), so you can't implement the Fredkin gate with it (NOT is just XOR with 1 as one input).

Your function looks a bit like the Fredkin gate, so I think you can't implement it with XOR and NOT, only. But if the Fredkin gate is a linear gate for you, you might solve it with this gate.

--
Frank Buss, fb@frank-buss.de
http://www.frank-buss.de, http://www.it4-systems.de
Reply to
Frank Buss

NAND and NOR gates can be used to build any logic function. They are the universal logic gates.

Reply to
Charles

That's the way the course instructor phrased the problem ;-)

...Jim Thompson

--
| James E.Thompson, P.E.                           |    mens     |
| Analog Innovations, Inc.                         |     et      |
| Analog/Mixed-Signal ASIC\'s and Discrete Systems  |    manus    |
| Phoenix, Arizona  85048    Skype: Contacts Only  |             |
| Voice:(480)460-2350  Fax: Available upon request |  Brass Rat  |
| E-mail Icon at http://www.analog-innovations.com |    1962     |

          The Democrats lost their souls a long time ago.
     It must have happened when they had their spines removed.
Reply to
Jim Thompson

That one requires either an AND or OR permitted in its output. You can't uncheck both. I think the OP wants something without either.

Jon

Reply to
Jonathan Kirwan

"Bernd Schneider" schrieb im Newsbeitrag news:g6dhrp$do7$ snipped-for-privacy@aioe.org...

Hello Bernd,

It looks for me that you have translated some technical content from German to English with a general dictionary. It's totally nonsense in my opinion to name XOR and NOT a linear gate. There are transfer gates of course. Maybe you want show me a link to the original German text and/or course material.

Best regards, Helmut Germany

Reply to
Helmut Sennewald

then it

'
t

e.

I'm thinking draw the K-map and get the job done.

Reply to
miso

snipped-for-privacy@sushi.com wrote in news: snipped-for-privacy@e53g2000hsa.googlegroups.com:

Yes, but the K-map diagram uses a lot of And and Or gates and this way I cannot achieve my constraint.

Regards, Bernd

Reply to
Bernd Schneider

"Helmut Sennewald" wrote in news:g6efud$ui$00 $ snipped-for-privacy@news.t-online.com:

No, I havent translated any text from German to English. In fact, I am not into electronics but a colleague of me has called these gates linear and And and Or non-linear gates. I think the idea is that the output of a linear gate is 1 with probability 1/2 whereas the output of a non-linear gate may differ (in case of an AND gate the probability that the output takes the value is indeed only 1/4). Following this definition the gates that I have specified are also linear and that let me hope that I can build them from only linear basic gates. My first gate is a multiplexer. I looked up in wikipedia how such a gate can be built from and and or gates, but there is no description if it can be build from XOR. The description of the MUX looks very, very similar to the decription of an XOR gate when it is build with only AND, NOT and OR gates, so that gives some hope, too.

Regards, Bernd

Reply to
Bernd Schneider

Jonathan Kirwan wrote in news: snipped-for-privacy@4ax.com:

Yes this is true. I hope it's possible to do so, but the more I look at it, it seems impossible to me.

Regards, Bernd

Reply to
Bernd Schneider

Jim Thompson wrote in news: snipped-for-privacy@4ax.com:

No, I came up with this problem myself.

Regards, Bernd

Reply to
Bernd Schneider

ElectronDepot website is not affiliated with any of the manufacturers or service providers discussed here. All logos and trade names are the property of their respective owners.