------+-----------+------------+
|        100 |       111 |        101 |
+------------+-----------+------------+

As an aggregate function:

CREATE TABLE vals2 (category VARCHAR(1), x INT);

INSERT INTO vals2 VALUES
 ('a',111),('a',110),('a',100),
 ('b','000'),('b',001),('b',011);

SELECT category, BIT_AND(x), BIT_OR(x), BIT_XOR(x) 
 FROM vals GROUP BY category;
+----------+------------+-----------+------------+
| category | BIT_AND(x) | BIT_OR(x) | BIT_XOR(x) |
+----------+------------+-----------+------------+
| a        |        100 |       111 |        101 |
| b        |          0 |        11 |         10 |
+----------+------------+-----------+------------+

No match:

SELECT BIT_AND(NULL);
+----------------------+
| BIT_AND(NULL)        |
+----------------------+
| 18446744073709551615 |
+----------------------+

URL: https://mariadb.com/kb/en/bit_and/https://mariadb.com/kb/en/bit_and/