Binary angular measurement: Difference between revisions

Revision as of 15:36, 5 July 2021

Revision as of 18:12, 5 July 2021

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The terms '''binary angular measurement''' ('''BAM''')<ref name="ship"/> and '''binary angular measurement system''' ('''BAMS''')<ref name="BAMS"/> refer to certain methodologies for representing and manipulating [[angle]]s using [[binary number|binary]] ([[number base|base]] 2) [[fixed-point arithmetic]]. The [[unit of measre|unit]] of angular measure used in those methods may be called '''binary radian''' ('''brad''') or '''binary degree'''.

These representation of angles are often used in [[numerical control]] and [[digital signal processing]] applications, such as robotics, navigation,<ref name=lap2004/> computer games,<ref name=sang1993/> and digital sensors.<ref name=para2005/> On the other hand, this system is not adequate for situations where the number of full turns must be measured, e.g. to monitor the rotation of vehicle wheels or of [[leadscrew]]s.

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===Signed fraction of turn===

Alternatively, the same ''n'' bits can also be interpreted as a signed integer in the range {−2^''n''−1 .. 2^''n''−1-1} in the [[two's complement]] convention. They can also be interpretes as a fraction of a full turn between −0.5 (inclusive) and +0.5 (exclusive) in signed fixed-point format, with the same scaling factor; or a fraction of half-turn between −1.0 (inclusive) and +1.0 (exclusive) with scaling factor 1/2^''n''−1.

Either way, these numbers can then be interpreted as angles between -180° (inclusive) and +180° (exclusive), with −0.25 meaning −90° and +0.25 meaning +90°. The result of adding or subtracting the numerical values will have the same sign as the result of adding or subtracting angles, once reduced to this range. This interpretation eliminates the need to reduce angles to the range [−π,+π] when computing [[trigonometric functions]].

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{{Uncategorized|date=July 2021}}