Using 3 input LUT's to Implement a Boolean Function

LUT. In summary, the conversation is about deriving an implementation for a function using the minimum possible number of three-input LUTs, with a given sum of min terms and a K map. Suggestions are given to use Shannon's expansion theorem to reduce the number of inputs for each LUT.
  • #1
blue2004STi
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0

Homework Statement


Consider the function f(w1,w2,w3,w4) = SUM( m(0, 1, 3, 6, 8, 9, 14, 15)). Derive an implementation using the minimum possible number of three-input LUTs.


Homework Equations


Where SUM(m(0, 1, 3, 6, 8, 9, 14, 15)) is the sum of the min terms, a Sum of Products that from a K map is (~w1*~w2*~w3)+(~w1*~w2*w4)+(w1*w2*~w3)+(w1*~w2*w3)+(~w1*w2*w3*~w4) Where ~w is "not w".

The Attempt at a Solution


Thus far all I can do is get the minimum cost solution from the K map, which I gave above. I guess I'm just a little confused as where to start considering a 3 input LUT has 8 stored values and 3 different inputs and one output. Any help will be beneficial! Thanks,

Matt
 
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  • #2
Noone have any ideas? I'm not looking for the answer just a push in the right direction. Thanks, Matt
 
  • #3
Use shannon's expansion theorem
 

Related to Using 3 input LUT's to Implement a Boolean Function

1. What is a 3 input LUT?

A 3 input LUT (Look-Up Table) is a digital logic element that can store and manipulate a Boolean function with 3 input variables. It contains a fixed table of inputs and outputs that allows it to perform logical operations on the inputs and produce a corresponding output.

2. How can 3 input LUT's be used to implement a Boolean function?

A 3 input LUT can be used to implement a Boolean function by assigning each input combination to a specific output value in the LUT. The LUT can then be programmed with the desired Boolean function, and when the inputs are applied, the corresponding output will be produced.

3. What are the advantages of using 3 input LUT's to implement a Boolean function?

Using 3 input LUT's to implement a Boolean function allows for a compact and efficient design as only one LUT is needed to store the entire function. It also allows for easy reprogramming of the function without changing the hardware. Additionally, LUT's can perform logical operations much faster than traditional logic gates.

4. Are there any limitations to using 3 input LUT's for Boolean functions?

One limitation of using 3 input LUT's is that it can only implement functions with 3 input variables. If a function requires more than 3 inputs, multiple LUT's would need to be used. Additionally, LUT's may not be able to implement more complex functions that require sequential logic.

5. How do you choose the appropriate 3 input LUT for a Boolean function?

The appropriate 3 input LUT for a Boolean function should have enough inputs to accommodate all the variables in the function. It should also have enough outputs to represent all the possible combinations of the function. The LUT should also have a fast enough response time to meet the requirements of the system it is being used in.

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