Generating a Boolean Cartesian product

In summary, The conversation discusses the need for a more efficient way to implement a set of ten inputs and twenty-five corresponding outputs. The suggestion is made to use AND gates, but the possibility of using multiplexers or a specialized chip is also considered. It is suggested to divide the problem into sub-problems and use a chip with six input pins and five output pins. The idea of using hex buffers and a multiplexer is also proposed, but datasheets are currently difficult to access. The need for all signals to be available at all times is mentioned.
  • #1
Bipolarity
776
2
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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  • #2
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.
 
  • #3
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
 
  • #4
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.
 
  • #5
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.
 

1. What is a Boolean Cartesian product?

A Boolean Cartesian product, also known as a Boolean matrix, is a mathematical operation that combines two or more sets of Boolean values to create a new set containing all possible combinations. It is often used in computer science and logic to generate truth tables.

2. How do you generate a Boolean Cartesian product?

To generate a Boolean Cartesian product, you need to first list out all the elements in each set. Then, create a grid with the same number of rows as the number of elements in the first set and the same number of columns as the number of elements in the second set. Finally, fill in the grid with all possible combinations of the elements from each set.

3. What is the purpose of generating a Boolean Cartesian product?

The purpose of generating a Boolean Cartesian product is to visualize all possible combinations of Boolean values from two or more sets. This can be useful in solving logic problems, creating truth tables, or testing different scenarios in computer programming.

4. Can a Boolean Cartesian product be generated with more than two sets?

Yes, a Boolean Cartesian product can be generated with any number of sets. The process is the same, but the grid will have more rows and columns to accommodate all the sets. For example, if you have three sets with 2, 3, and 4 elements respectively, the grid would have 2 x 3 x 4 = 24 cells.

5. Are there any tools or programs that can help with generating a Boolean Cartesian product?

Yes, there are many online tools and programs that can help with generating a Boolean Cartesian product. Some popular ones include Truth Table Generator, Logic Friday, and Boolean Algebra Calculator. These tools allow you to input the sets and automatically generate the Cartesian product for you.

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