2^k - 1 as Output of a Circuit with 3 k-bit Inputs

[Schfra]

If I have a circuit with 3 inputs with k bits, A, B and C, how can I get the output to be 2^k - 1 using relatively standard components? And, or, not, mux, decoder, adder, etc...

This is for part of an exercise that I’m doing. I couldn’t find anything in the notes to help. Could anybody give some advice about how to deal with powers in a situation like this?

 

[donpacino]

Is this for homework?

Assuming it is, have you ever worked with truth tables?
Why don't you draw the truth table mapping your inputs to outputs.
Also I am making an assumption that the output is digital.

 

[Schfra]

Is this for homework?

Assuming it is, have you ever worked with truth tables?
Why don't you draw the truth table mapping your inputs to outputs.
Also I am making an assumption that the output is digital.

This question isn’t a homework question but I think I’ll be able to figure out a homework problem I’m working on if I get this figured out.

And yes it’s digital.

I’m not quite sure how to make a truth table with inputs that have k bits.

 

[berkeman]

Welcome to the PF.

This question isn’t a homework question but I think I’ll be able to figure out a homework problem I’m working on if I get this figured out.

It's still a schoolwork-type question, so it belongs in the schoolwork forums. I've moved your thread for you.

I'm not quite sure how to make a truth table with inputs that have k bits.

You should be able to use your study materials or even Google Images to see how to do this. Your first 9 columns are the 3 input variables with their 3 bits apiece, and the column(s) to the right are the corresponding outputs.

 

[Schfra]

Welcome to the PF.

It's still a schoolwork-type question, so it belongs in the schoolwork forums. I've moved your thread for you.

You should be able to use your study materials or even Google Images to see how to do this. Your first 9 columns are the 3 input variables with their 3 bits apiece, and the column(s) to the right are the corresponding outputs.

Thanks, I must have missed the section for engineering homework.

Why 3 bits apiece if the variables are all k bits? I think the unknown number of bits is throwing me off.

 

[berkeman]

If I have a circuit with 3 inputs with k bits, A, B and C, how can I get the output to be 2^k - 1

hy 3 bits apiece if the variables are all k bits? I think the unknown number of bits is throwing me off.

Maybe I'm misunderstanding your original problem statement. I thought you meant you had 3 inputs and each had bits A, B and C. But I guess you mean you have 3 input variables A, B, and C, each with k bits apiece? In that case, what do you mean that you want the output to be 2^k - 1? Have you posted the full problem statement? Was there any diagram with it?