Convert base 10 to base 2 in SQL Server for very large numbers

On SQL Server 2017 I have a base 10 number of type DECIMAL(38,0) which I need to convert to its base 2 representation.

This works fine for smaller numbers, but fails with the target order of magnitude:

DECLARE @var1 DECIMAL(38, 0) = 2679226456636072036565806253187530752;
WITH A
     AS (SELECT @var1 AS NUMBER, 
                CAST('' AS VARCHAR(125)) AS BITS
         UNION ALL
         SELECT CAST(ROUND(NUMBER / 2, 0, 1) AS DECIMAL(38, 0)),
                CAST(BITS + CAST(NUMBER % 2 AS VARCHAR(125)) AS VARCHAR(125))
         FROM A
         WHERE NUMBER > 0)
     SELECT NUMBER, 
            RIGHT(REPLICATE('0', 125) + CASE
                                            WHEN BITS = ''
                                            THEN '0'
                                            ELSE REVERSE(BITS)
                                        END, 125) AS BIN_VALUE
     FROM A
     WHERE NUMBER = 0;

The error message reads Msg 8115, Level 16, State 2, Line 2 Arithmetic overflow error converting expression to data type numeric.

I have also tried other approaches, but each has failed due to the magnitude of the original value. Any help with performing this conversion is greatly appreciated.

Answer

--DECLARE @var1 DECIMAL(38, 0) = 2679226456636072036565806253187530752;
DECLARE @var1 DECIMAL(38, 0) = 99999567999999999999999999999999999999;
WITH A
AS 
(
    SELECT @var1 AS NUMBER, 
        CAST('' AS VARCHAR(130)) AS BITS
    UNION ALL
    SELECT CAST(
         cast(round(NUMBER*0.1, 0, 1) as decimal(38,0))*5 --high part
            + 
            round(cast('0.'+right(NUMBER, 1) as decimal(10,2))* 5, 0, 1) --low part
         --ROUND(NUMBER * 0.5, 0, 1)
         AS DECIMAL(38, 0)),
         CAST(BITS + CAST(NUMBER % 2 AS VARCHAR(125)) AS VARCHAR(130))
     FROM A
     WHERE NUMBER > 0
)
SELECT NUMBER, 
        RIGHT(REPLICATE('0', 130) + CASE
                                        WHEN BITS = ''
                                        THEN '0'
                                        ELSE REVERSE(BITS)
                                    END, 130) AS BIN_VALUE
FROM A
WHERE NUMBER = 0
option (maxrecursion 0);