Mysql xor operator does not properly work, when one of condition is null

I need to add a clause for select where either a record equals the value or equals null.

select * 
from table 
where column = 123 or column is null;

As a result I get

|column|
  123
  123
  null
  null

When I try to use xor

select * 
from table 
where column = 123 xor column is null;

I get either only 123 records

|column|
  123
  123

or, if there is no 123, I got nothing

|column|

But I need, when there is no 123 records to get only null ones. So basically my desired result will be:

|db column|      |column with 123 clause|    |column with 125 clause|
  123                     123                        null
  123                     123                        null
  null
  null
  124

Could you please help me with this issue?

Solution

You want the third and fourth row returned if the first and second are not returned, right? This cannot be expressed with a simple where clause. Try

select * from table where column=123
  or column is null and not exists
     (select * from table where column=123)

Regarding your xor observation: I assume that

column=123 xor column is null

is equivalent to

column=123 and column is not null or
column<>123 and column is null

But when column = null, the expression column<>123 is false, therefore the overall condition is also false.