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Binary logarithm
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===Sports scheduling=== In competitive games and sports involving two players or teams in each game or match, the binary logarithm indicates the number of rounds necessary in a [[single-elimination tournament]] required to determine a winner. For example, a tournament of {{math|4}} players requires {{math|1=log<sub>2</sub>{{hsp}}4 = 2}} rounds to determine the winner, a tournament of {{math|32}} teams requires {{math|1=log<sub>2</sub>{{hsp}}32 = 5}} rounds, etc. In this case, for {{mvar|n}} players/teams where {{mvar|n}} is not a power of 2, {{math|log<sub>2</sub>{{hsp}}''n''}} is rounded up since it is necessary to have at least one round in which not all remaining competitors play. For example, {{math|log<sub>2</sub>{{hsp}}6}} is approximately {{math|2.585}}, which rounds up to {{math|3}}, indicating that a tournament of {{math|6}} teams requires {{math|3}} rounds (either two teams sit out the first round, or one team sits out the second round). The same number of rounds is also necessary to determine a clear winner in a [[Swiss-system tournament]].<ref>{{citation|title=Introduction to Physical Education and Sport Science|first=Robert|last=France|publisher=Cengage Learning|year=2008|isbn=978-1-4180-5529-5|page=282|url=https://books.google.com/books?id=dH2nB1CX2SMC&pg=PA282}}.</ref>
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