Bit (of data): Examples

In the game “20 ques­tions”, one player (the “leader”) thinks of a con­cept, and the other play­ers ask 20 yes-or-no ques­tions in at­tempts to guess that con­cept. In this game, the play­ers ex­tract 20 bits of data from the leader, which (if the ques­tions are se­lected wisely) is enough data to sin­gle out one con­cept from a set of roughly one mil­lion con­cepts (1048576, to be pre­cise).

Three bits of data are re­quired to spec­ify one of the hands of one of your biolog­i­cal grand­par­ents: One bit for “ma­ter­nal” or “pa­ter­nal”, one bit for “male” or “fe­male,” one bit for “left” or “right.”

The pres­i­dent of the United States of Amer­ica is se­lected from a set of about 320,000,000 peo­ple. This se­lec­tion en­codes roughly 28 bits of data. Where do those bits come from? Between 14 and 12 of the pop­u­la­tion is el­i­gible for the pres­i­dency, so 1-2 bits come from con­straints on who is al­lowed to be pres­i­dent. Another ~1 bit comes from the vot­ers in the pres­i­den­tial elec­tion (when one can­di­date is se­lected from a set of two fi­nal­ists). 2-4 more bits come from the pri­mary elec­tions (when the two fi­nal­ists are se­lected from a set of ~4-32). How­ever, most of the bits that go into choos­ing the pres­i­dent — 21 or more of them — come from self-se­lec­tion and pri­vate politick­ing.