create table t1(a bit(1), b int auto_increment ,id int,  index(a,b));
insert into t1 values(1,null,1);
insert into t1 values(1,null,2);
insert into t1 values(0,null,3);
insert into t1 values(0,null,4);
select a+0, b as auto_increment , id from t1 order by id;
a+0	auto_increment	id
1	1	1
1	2	2
0	1	3
0	2	4
drop table t1;
create table t1(a int auto_increment, b bit(5) ,id int, index (b,a));
insert into t1 values(null,b'1',1);
insert into t1 values(null,b'1',2);
insert into t1 values(null,b'11',3);
insert into t1 values(null,b'11',4);
select a as auto_increment, b+0, id from t1 order by id;
auto_increment	b+0	id
1	1	1
2	1	2
1	3	3
2	3	4
drop table t1;
create table t1(a bit(1), b int auto_increment , c bit(1) , d bit(1), id int,index(a,c,b,d));
insert into t1 values(1,null,1,1,1);
insert into t1 values(1,null,1,1,2);
insert into t1 values(0,null,1,1,3);
insert into t1 values(1,null,0,1,4);
select a+0, b as auto_increment, c+0, d+0, id from t1 order by id;
a+0	auto_increment	c+0	d+0	id
1	1	1	1	1
1	2	1	1	2
0	1	1	1	3
1	1	0	1	4
drop table t1;
CREATE TABLE t1 (b BIT(1), pk INTEGER AUTO_INCREMENT PRIMARY KEY);
ALTER TABLE t1 ADD INDEX(b,pk);
INSERT INTO t1 VALUES (1,b'1');
ALTER TABLE t1 DROP PRIMARY KEY;
select b+0, pk as auto_increment from t1;
b+0	auto_increment
1	1
DROP TABLE t1;