Binary angular measurement: Difference between revisions

Revision as of 21:29, 26 February 2024

Revision as of 21:57, 27 February 2024

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==Representation==

===Unsigned fraction of turn===

In this system, an angle is represented by an ''n''-[[bit]] unsigned binary number in the sequence 0, ..., 2^''n''−1 that is interpreted as ana multiple of 1/2^''n'' of a full turn; that is, 360/2^''n'' degrees or 2π/2^''n'' radians. The number can also be interpreted as a fraction of a full turn between 0 (inclusive) and 1 (exclusive) represented in binary fixed-point format with a scaling factor of 1/2^''n''. Multiplying that fraction by 360° or 2π gives the angle in [[degree (angle)|degree]]s in the range 0 to 360, or in [[radian]]s, in the range 0 to 2π, respectively.

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.