Binary angular measurement: Difference between revisions

Revision as of 15:30, 5 July 2021

Revision as of 15:32, 5 July 2021

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For example, with ''n'' = 8, the binary integers (00000000)₂ (fraction 0.00), (01000000)₂ (0.25), (10000000)₂ (0.50), and (11000000)₂ (0.75) represent the angular measures 0°, 90°, 180°, and 270°, respectively.

A main advantage of this system is that the addition or subtraction of the integer numeric values with the ''n''-bit arithmetic used in most computers produces results that are consistent with the geometry of angles. Namely, the integer result of the operation is obtained [[modular arthmeticarithmetic|modulo]] 2^''n'' corresponds to the fact that the angles that differ by an integer number of full turns (2^''n'' units) are equivalent. Thus one does not need to explicitly test or handle the wrap-around, as one must do when using other representations (such as number of degrees or radians in floating-point).<ref name=harg2019/>

===Signed fraction of turn===