SQL - Find the binary representation from the place of '1's - sql

Question

It is really hard to find a good title for this.
Here is the question: I have a SELECT query GROUP BY a field which returns me up to three values (1,2,3). These values are representing the positions of '1' in a binary number.
In other words:
Query Output | Reult
0,1,2 | 7 (111)
1,2 | 6 (110)
3 | 1 (001)
- | 0 (000)
Ok, I know it is easy. But there are two constraints. First, I want a query not a function/store procedure. Second, the result should be a string (like '010') not the number.
I found the solution for integer value, but not the string (varchar)
SELECT COALESCE(sum(power(2, field)), 0) AS test FROM (
SELECT field FROM myTable GROUP BY field) a
I am using SQL server 2008, just in case.
I also have this solution, but this one cannot be extended to bigger number of outputs:
SELECT output =
CASE TEST
WHEN 0 THEN '000'
WHEN 1 THEN '001'
WHEN 2 THEN '010'
WHEN 3 THEN '011'
WHEN 4 THEN '100'
WHEN 5 THEN '101'
WHEN 6 THEN '110'
WHEN 7 THEN '111'
END
FROM(
select COALESCE(sum(power(2, 3 - field)), 0) as test from (
select field from myTable group by field) a) b

Answer 1

You can use binary and and string concatenation:
select (case when test&4 > 0 then '1' else '0' end) +
(case when test&2 > 0 then '1' else '0' end) +
(case when test&1 > 0 then '1' else '0' end)
from (select 6 as test) t;
If you are allergic to case statements, you could do this:
select CHAR(ascii(0) + (test&4)/4) +
CHAR(ascii(0) + (test&2)/2) +
CHAR(ascii(0) + (test&1)/1)
from (select 6 as test) t