How can permutations help with logic gates and circuit design?

In summary, the conversation involved a discussion on permutations and combinations, with the mention of a potential application in working with a circuit board. The homework involved creating a table to show different logic gate combinations. It was clarified that no factorials arise in this context, but the number of combinations can be determined by multiplying the number of distinct things by the number of possible states for each thing. The conversation concluded with the confirmation of the general rule for determining the number of combinations in a given scenario.
  • #1
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Hello,

today in class we started a topic on permutations and combinations and I have come across a way in which it could be of use to me whilst working with 'logictutor' (a premade circuit board used to teach simple logic circuits).

We have an experiment tomorrow where we will investigate different logic gates and build a decade counter and whilst my question isn't about that, I think it would be nice to show the permutations of inputs.

Homework Statement



There are four switches on the board that control the input to a seven segment display and I need to fill out a table that shows the position of each switch and what the display will show.

Homework Equations





The Attempt at a Solution



There are 4! permutations possible for 4 items but in my situation each item can be either on or off.

I hope this doesn't translate to their being 8! permutations otherwise I'm going to be up all night on excel making tables.

So how do I model this problem to show the number of permutations? I suppose I would like to know because as truth tables get bigger and bigger it could be a quick check to show I have every possibility.

Thanks! (I hope my question is clear)
 
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  • #2
No factorials arise in this context. You are not shuffling the order of things or selecting fixed size subsets.
If you wanted to list the combinations in terms of how many switches are on then you would see some factorials, but that's not an interesting way to list them here.
You have N distinct things, each of which can be in any of R states. How many possible combinations of states?
If you're not sure, start with N=1 and work up.
 
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  • #3
haruspex said:
No factorials arise in this context. You are not shuffling the order of things or selecting fixed size subsets.
If you wanted to list the combinations in terms of how many switches are on then you would see some factorials, but that's not an interesting way to list them here.
You have N distinct things, each of which can be in either of R states. How many possible combinations of states?
If you're not sure, start with N=1 and work up.


One switch has 2 different combinations of states.

Two switches have four different combinations of states.

Three switches have 8 different combinations of states.

Looking at this, the general rule appears to be number of combinations = rN

For my four switch scenario there should be 16 combinations - Which is precisely how many I could come up with :)

Thank you!
 
  • #4
Yep, now you've got it.
 

1. What are permutations and why are they important in science?

Permutations refer to the different ways in which a set of objects can be arranged in a specific order. In science, permutations are important because they allow us to consider all possible outcomes in a given situation, which is crucial for making accurate predictions and understanding complex systems.

2. How are permutations used in genetics and DNA sequencing?

In genetics, permutations are used to determine the possible combinations of alleles in a genotype. In DNA sequencing, permutations are used to identify the specific order of nucleotides in a DNA strand, which is important for understanding genetic information and identifying potential mutations.

3. What are logic gates and how do they work?

Logic gates are electronic devices that perform logical operations on one or more binary inputs to produce a single binary output. They are the building blocks of digital circuits and can be combined to create complex logical functions. They work by using transistors to control the flow of electricity and produce different output values based on the input values.

4. How are logic gates used in computer programming and circuit design?

In computer programming, logic gates are used to perform Boolean logic operations, which are essential for decision making and controlling the flow of code. In circuit design, logic gates are used to create electronic circuits that can perform a variety of functions, such as data processing, memory storage, and communication.

5. What is the relationship between permutations and logic gates?

Permutations and logic gates are closely related in that both involve the manipulation and arrangement of different elements. In science and technology, permutations are used to explore all possible outcomes, while logic gates are used to process and manipulate information to achieve a desired result. In some cases, logic gates can be seen as a physical representation of permutations, as they allow us to control the arrangement and flow of electrical signals in a circuit.

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