SET enable_seqscan = off;
CREATE TABLE t (val bit(3));
INSERT INTO t (val) VALUES (B'000'), (B'100'), (B'111'), (NULL);
CREATE INDEX ON t USING hnsw (val bit_hamming_ops);
INSERT INTO t (val) VALUES (B'110');
SELECT * FROM t ORDER BY val <~> B'111';
 val 
-----
 111
 110
 100
 000
(4 rows)

SELECT COUNT(*) FROM (SELECT * FROM t ORDER BY val <~> (SELECT NULL::bit)) t2;
 count 
-------
     4
(1 row)

DROP TABLE t;