I modified your code to make it more useful.
DECLARE @S NVARCHAR(MAX)
DECLARE @result INT
DECLARE @count_me NVARCHAR(MAX)
The string to be searched.
SET @S = '1101001001110101'
The character to be counted.
SET @count_me = '00'
Replace the character to be counted with empty string,
and subtract the lengths.
SET @result = (LEN(@s) - LEN(REPLACE(@s,@count_me,'')) )/LEN(@count_me)
Do something with the result