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';
SELECT COUNT(*) FROM (SELECT * FROM t ORDER BY val <~> (SELECT NULL::bit)) t2;

DROP TABLE t;