how to solve this question

i need to implement a sequential circuit that has two outputs
the first recognizes 1,4,5,9
the second one recognizes 12,13,14,15
i need build this one using a PROM and a shift register

Why do you need a shift register if you have a PROM?

to be onest..

i think that a shift register is just a slow input line
it proceeds in each Clock pulse were in normal line they data comes straight away.


i was required to use it in the question

i dont have any idea of how to build this thing

when i tried to build the situation table
i came to the conclusion that building it in the normal way with flip flops
its impossible.its a 4 bit number
there are lots of possibilities
it would take me hours to write each one

i think they intended for some other solution

what should i do??

What's the problem? The PROM watches the Shift Register. Each time the outputs of the shift regiser change, the outputs of the PROM change telling you that the quantity in the shift register matches the conditions.

That's either the solution or I don't understand the problem statement.