a question about building a multiplicator using a PROM

[transgalactic]

my question is:
design a binary multiplicator which input two numbers
the first one called "X" has 3 bits length x2x1x0
the second number is called "Y" has two bits y1y0

also
Y<=2
and X gets the values 2,3,6,7 only

implement the system using a PROM 2^4 X2
write down the programming table of PROM in the relevant addresses.

i cant understand the solution that i was given
the table that i was given dont have any sense
can some one explain to me those table??

https://img260.imageshack.us/my.php?image=img86801nz4.jpg

 

[FvM]

As a difficulty, there isn't any explanation. Also in the second table, three lines with zero output are omitted as well as the last four lines in both tables that have no existing input coding.

The most simple way to understand the tables is to solve the problem by yourself. You probably get similar tables and then you understand.

As a hint: The highest number, that must be represented in the result is 2*7, thus you need 4 bits for the results. As the PROM building block has two bits output, two PROMs are required. In the solution, #1 is the code table for the lower output bits (S1, S0) and #2 is the code table for the upper outbit bits (S3, S2).

 

[transgalactic]

i cant ubderstand the stucture
i cant see the multilication proccess in the tables

 

[FvM]

A look-up table decoding all 5 input bits would have 32 rows. Because of the range limitations, only 4 of the 5 are relevant as address bits, thus the table reduces to 16 rows. As I mentioned, some of these 16 are omitted, but all rows with nonzero output are shown in the solution.

 

[transgalactic]

i cant see that the inputs are the same
in the first line on the first table the inputs are zeros
and on the second table
there are dont care
not the same thing.

i still cant understand why cant we put a big box with 5 inputs
and 4 outputs

i dont know whats LUT
i looked up in google and it says that it a table
can you explain to me with simpler terms
why we need to split the whole thing into to components??

nobody sayd that its 2^4 X 2

you told me that its because of some limitation in addressess
that why we are splitting into to components
but i cant see it in the question
how should i recognize that there is an address limitation??