How to calculate an arbitrary decoder?

Question

Programming

there is a truth table inputs a,b outputs x1,x2,x3,x4
a,b x1,x2,x3,x4
00 0 0 0 1
10 0 1 1 0
01 1 0 1 0
11 1 0 1 0
can't find how to access it to build a decoder on AND OR NOT elements, there are different examples: a decimal decoder, hexadecimal, for a seven-segment indicator, but there is no methodology for how to calculate, there is only for cases where there are fewer outputs than inputs ( digteh.ru/digital/SintSxem.php ), how to cross the information available to obtain the desired result, I do not understand,
please kick in which direction to read

Answer 1

please kick in which direction to read

In my opinion, knowledge of the truth tables of elementary functions and the ability to combine them is enough here.
My version:
The gates can be implemented in different ways (for example, output x4 from x3 or from inputs).

Answer 2

if 2 inputs and 4 outputs is a bit strange situation, but it is not fundamentally complicated, is the decoder planned to be built in hardware or software?
if in hardware, then there are 4 blocks of the simplest and / or 00 10 01 11, respectively, from each of them there will be a connection to 4 "outputs". If programmatically, there are no more problems.