Etymology
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bit (n.1)

"small piece," c. 1200; related Old English bite "act of biting," and bita "piece bitten off," which probably are the source of the modern words meaning "boring-piece of a drill" (the "biting" part, 1590s), "mouthpiece of a horse's bridle" (mid-14c.), and "a piece (of food) bitten off, morsel" (c. 1000). All from Proto-Germanic *biton (source also of Old Saxon biti, Old Norse bit, Old Frisian bite, Middle Dutch bete, Old High German bizzo "biting," German Bissen "a bite, morsel"), from PIE root *bheid- "to split."

Meaning "small piece, fragment" of anything is from c. 1600. Sense of "short space of time" is 1650s. Theatrical bit part is from 1909. Money sense "small coin" in two bits, etc. is originally from the U.S. South and the West Indies, in reference to silver wedges cut or stamped from Spanish dollars (later Mexican reals); transferred to "eighth of a dollar."

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bit (n.2)

computerese word, 1948, coined by U.S. computer pioneer John W. Tukey, an abbreviation of binary digit, probably chosen for its identity with bit (n.1).

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bitmap (n.)
1973, in computer jargon, from bit (n.2) + map. Literally, a map of bits.
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bitsy (adj.)
1883, from plural of bit (n.1) or a variant of bitty.
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BitTorrent 
peer-to-peer file sharing protocol, implemented in 2001, from bit (n.2) in the computing sense + torrent.
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bitty (adj.)

"small," 1898, baby-talk, from bit (n.1) + -y (2). Earlier "made up of little bits," 1873.

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tidbit (n.)
1630s, probably from dialectal tid "fond, solicitous, tender" (perhaps by influence of tit (n.2)) + bit (n.1) "morsel."
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bitt (n.)
nautical, "strong post to which cables are made fast" (usually in plural, bitts), 1590s, of uncertain origin; compare Old Norse biti "crossbeam." Probably somehow related to bit (n.1).
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byte (n.)
"unit of digital information in a computer," typically consisting of eight bits, 1956, American English; see bit (n.2). Reputedly coined by German-born American computer scientist Werner Buchholz (b. 1922) at IBM.
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