I have the following exercise:

Design a circuit that takes a 2 bit binary and makes it x^3 (x cubed), using a decoder
of your choice.

I thoguht to do it with a 3 to 8 decoder, because I have 2 bits of input, and 4 bits of output, since the largest output is 11011 (which is 27 in decimal).

I have managed to get to a truth table. Input = x0x1x2. Output=a,b,c,d,e.

x1 x1 x2 a b c d e
0 0 0 0 0 0 0 0
0 0 1 0 0 0 0 1
0 1 0 0 1 0 0 0
0 1 1 1 1 0 1 1

However, I am not quite sure what should I do now. I have to get to a function to represent it in gates? How can I make a karnaugh map from that table?

I am aware that I would have to add three more outputs to the 3 to 8 decoder, but they will be just "don't cares".

Your help is appriciated.

 

Hello nerazzurri10

You say this statement:
Design a circuit That Takes a 2 bit binary and makes it x ^ 3 (x cubed), using a decoder of your choice.

Later You ask:
I have to get to a function to Represent it in gates?
look at the blue underlined words in your statement
If you want to do with logic gates the Decoder, the answer is YES
but if not,
You can select a decoder chip

How can I make a Karnaugh map from That table?
There is a computer program that could help You:
Boole-Deusto. look for it in google.com, download it, and install it on your PC.
It is relatively easy to use.

 

Hello Mr. Carlos,

Thank you for your kind answer.

It might be better for me to do the karnough map by myself rather than with a software, since in the exam I won't be able to use it. It will be helpful in the future, though, so I thank you.