A de Bruijn sequence is the shortest possible loop that contains every short string exactly once. For 3-bit strings over {0,1} that loop is just 8 bits long — and a sliding 3-bit window reads all eight of 000…111 with none repeated. Slide the window around the ring and watch it tick them off.
A B(2,3) de Bruijn sequence is built here by the standard recursive (Lyndon-word) construction, yielding the length-8 cyclic string 00010111. Because it is de Bruijn, sliding a 3-bit window around the ring produces every one of the 2³=8 binary triples exactly once. A fail-loud self-check throws unless the sequence has length 8 AND the eight windowed triples form all of {000,001,…,111} with no repeat — the defining property, verified, not assumed.
B(2,3) is one specific de Bruijn sequence (rotations and the 0/1 swap give others); the CONSTRUCTION and the all-8-unique proof are exact. de Bruijn’s 1946 count k!^(k^(n−1))/kⁿ of such sequences is cited, not enumerated here.