how to understand binary logic

and operation
:neocat_hug: = :neocat:
:neofox_hug_cat: = :neocat:
:neocat_hug_fox: = :neocat:
:neofox_hug: = :neofox:

or operation
:neocat_hug: = :neocat:
:neofox_hug_cat: = :neofox:
:neocat_hug_fox: = :neofox:
:neofox_hug: = :neofox:

xor operation
:neocat_hug: = :neocat:
:neofox_hug_cat: = :neofox:
:neocat_hug_fox: = :neofox:
:neofox_hug: = :neocat: