Generating a Boolean Cartesian product

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Discussion Overview

The discussion revolves around finding an efficient method to implement a Boolean Cartesian product for ten inputs resulting in twenty-five outputs. Participants explore various approaches, including the use of AND gates, multiplexers, and specialized chips, while considering the efficiency and complexity of different implementations.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant suggests using 25 AND gates as a brute force method to achieve the desired outputs, questioning if there might be a simpler approach.
  • Another participant agrees that 25 outputs correspond to at least 25 logic gates or an integrated circuit (IC) with similar capacity, noting that while AND gates are a natural choice, alternative gate implementations could be explored.
  • A participant proposes dividing the problem into sub-problems, suggesting that a chip could take inputs A, V, W, X, Y, Z and produce outputs AV, AW, AX, AY, AZ.
  • Another participant mentions the existence of hex buffers/line drivers with tristate outputs that may fulfill the requirements, although they express difficulty in finding datasheets for specific components.
  • One participant emphasizes that if all signals need to be available at all times and outputs must change with input changes, the use of 25 AND gates may be the only viable solution given the lack of leniency in specifications.

Areas of Agreement / Disagreement

Participants express differing views on the best approach to implement the Boolean Cartesian product, with no consensus on a single method or solution. Some advocate for the brute force method using AND gates, while others explore the potential for more complex configurations with multiplexers or specialized chips.

Contextual Notes

Participants have not provided specific assumptions or constraints regarding the implementation requirements, and there is uncertainty about the availability of suitable chips or components that could simplify the design.

Bipolarity
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I basically am looking for an efficient way to implement the following:
I have ten inputs, {A,B,C,D,E,V,W,X,Y,Z}. I have twenty-five outputs that I need to implement:
{AV,AW,AX,AY,AZ, BV,BW,BX,BY,BZ, CV,CW,CX,CY,CZ, DV,DW,DX,DY,DZ, EV,EW,EX,EY,EZ}.

Obviously, a brute force way to do this would be to just use 25 AND gates. That costs me about 7 chips. Perhaps there is a simpler method I am overlooking that someone can suggest? Maybe with multiplexers etc. ? Or maybe there is a specialized chip to perform this kind of "Cartesian product" ?

Any ideas guys? Really appreciate it!

Thanks!

BiP
 
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You need 25 different outputs, this corresponds to at least 25 different logic gates or an IC with at least that amount of logic inside. AND gates are a natural choice, if you can implement other gates cheaper/easier a more complicated setup could be interesting.
 
mfb said:
You need 25 different outputs, this corresponds to at least 25 different logic gates or an IC with at least that amount of logic inside. AND gates are a natural choice, if you can implement other gates cheaper/easier a more complicated setup could be interesting.

Certainly there is no single chip I know of with 25 different outputs. But what if the problem was divided into 5 sub-problems, say one is just finding AV,AW,AX,AY,AZ ? Then is there a chip that takes as input A,V,W,X,Y,Z (six pins) and outputs AV,AW,AX,AY,AZ (5 pins). Surely some chip performs this function?

BiP
 
Then is there a chip that takes as input A,V,W,X,Y,Z (six pins) and outputs AV,AW,AX,AY,AZ (5 pins). Surely some chip performs this function?

There's any number of hex buffers/linedrivers with tristate output and enable pin that are mighty close to what you describe.
I'm having trouble finding datasheets - seems search engines only return that no-good pesky alldatasheets link anymore.
Try 74**368

and a one of several multiplexer like 74**451

sorry i can't get to datasheets anymore. Revolt of the machines, i guess.
 
Bipolarity said:
Obviously, a brute force way to do this would be to just use 25 AND gates.
If you want all signals available all of the time, and outputs to change whenever an input changes, I can't see any other way of doing it. You haven't indicated more lenient specs.