This has been answered for you already, twice, in the past 14 hours on Stack Overflow, including a pretty lengthy and explanatory yet unappreciated (and since deleted) answer by me. Let's keep it simple:
To update the column, you need to use an explicit conversion:
UPDATE table SET column = CONVERT(varbinary(8), '1') WHERE ...;
'1' is stored in varbinary as
0x31. If you select from the table, that's what you'll see. To see it as you entered it, you need to convert it back:
SELECT column, CONVERT(varchar(32), column) FROM table WHERE ...;
If you don't like having to convert a string to and from varbinary, stop using varbinary to store values like 0 and 1 - you should be using a bit column in the first place. As has been suggested multiple times. If you can't change it, you'll need to learn how to work with it. There are no short cuts.