A case statement? For example:
CREATE TABLE #BIT (ID INT IDENTITY(1,1),
       BitValue1 BIT,
       BitValue2 BIT);
GO

INSERT INTO #BIT
VALUES (1,1),
       (1,0),
       (0,1),
       (0,0);
GO

SELECT *,
       CASE WHEN BitValue1 = 1 OR BitValue2 = 1 THEN 1 ELSE 0 END AS OrValue,
       CASE WHEN BitValue1 = 0 AND BitValue2 = 0 THEN 0
            WHEN BitValue1 = 1 AND BitValue2 = 1 THEN 0
            ELSE 1 END AS XorValue
FROM #BIT;

DROP TABLE #BIT;
GO