对于非常大的数字，在SQL Server中将基数10转换为基数2

Question

在SQL Server2017上，我有一个DECIMAL(38,0)类型的基数为10的数字，我需要将其转换为基数为2的表示形式。

这对于较小的数字可以很好地工作，但对于目标数量级则失败：

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;

错误消息显示为Msg 8115, Level 16, State 2, Line 2 Arithmetic overflow error converting expression to data type numeric.

我还尝试了其他方法，但由于原始值的大小，每种方法都失败了。对执行此转换的任何帮助都是非常感谢的。

Answer 1

--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);