The terms binary angular measurement (BAM) and binary angular measurement system (BAMS) refer to certain methodologies for representing and manipulating

angle In Euclidean geometry, an angle is the figure formed by two Ray (geometry), rays, called the ''Side (plane geometry), sides'' of the angle, sharing a common endpoint, called the ''vertex (geometry), vertex'' of the angle. Angles formed by two ...

s using

binary Binary may refer to: Science and technology Mathematics * Binary number, a representation of numbers using only two digits (0 and 1) * Binary function, a function that takes two arguments * Binary operation, a mathematical operation that t ...

( base 2)

fixed-point arithmetic In computing, fixed-point is a method of representing fractional (non-integer) numbers by storing a fixed number of digits of their fractional part. Dollar amounts, for example, are often stored with exactly two fractional digits, representi ...

. The

unit Unit may refer to: Arts and entertainment * UNIT, a fictional military organization in the science fiction television series ''Doctor Who'' * Unit of action, a discrete piece of action (or beat) in a theatrical presentation Music * ''Unit'' (alb ...

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 Numerical control (also computer numerical control, and commonly called CNC) is the automated control of machining tools (such as drills, lathes, mills, grinders, routers and 3D printers) by means of a computer. A CNC machine processes a pi ...

and

digital signal processing Digital signal processing (DSP) is the use of digital processing, such as by computers or more specialized digital signal processors, to perform a wide variety of signal processing operations. The digital signals processed in this manner are ...

applications, such as robotics, navigation, computer games, and digital sensors. 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 A leadscrew (or lead screw), also known as a power screw or translation screw,Bhandari, p. 202. is a screw (simple machine), screw used as a linkage (mechanical), linkage in a machine, to translate Rotation, turning motion into linear motion. ...

Representation

Unsigned fraction of turn

In this system, an angle is represented by an ''n''-

bit The bit is the most basic unit of information in computing and digital communications. The name is a portmanteau of binary digit. The bit represents a logical state with one of two possible values. These values are most commonly represente ...

unsigned binary number in the sequence 0, ..., 2^''n''−1 that is interpreted as an 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 Degree may refer to: As a unit of measurement * Degree (angle), a unit of angle measurement ** Degree of geographical latitude ** Degree of geographical longitude * Degree symbol (°), a notation used in science, engineering, and mathematics ...

s in the range 0 to 360, or in

radian The radian, denoted by the symbol rad, is the unit of angle in the International System of Units (SI) and is the standard unit of angular measure used in many areas of mathematics. The unit was formerly an SI supplementary unit (before that c ...

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. The 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 automatically reduced modulo 2^''n'', matching the fact that angles that differ by an integer number of full turns 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).

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 Two's complement is a mathematical operation to reversibly convert a positive binary number into a negative binary number with equivalent (but negative) value, using the binary digit with the greatest place value (the leftmost bit in big- endian ...

convention. They can also be interpreted 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 when computing

trigonometric functions In mathematics, the trigonometric functions (also called circular functions, angle functions or goniometric functions) are real functions which relate an angle of a right-angled triangle to ratios of two side lengths. They are widely used in all ...

References

{{reflist, refs= {{cite web , title=Binary angular measurement , url=http://www.tpub.com/content/fc/14100/css/14100_314.htm , archive-url=https://web.archive.org/web/20091221160257/http://www.tpub.com/content/fc/14100/css/14100_314.htm , archive-date=2009-12-21 {{cite web , title=Binary Angular Measurement System , work=acronyms.thefreedictionary , url=http://acronyms.thefreedictionary.com/Binary+Angular+Measurement+System {{cite web , title=Angles, integers, and modulo arithmetic , author-first=Shawn , author-last=Hargreaves , author-link=:pl:Shawn Hargreaves , publisher=blogs.msdn.com , url=http://blogs.msdn.com/shawnhar/archive/2010/01/04/angles-integers-and-modulo-arithmetic.aspx , access-date=2019-08-05 , url-status=live , archive-url=https://web.archive.org/web/20190630223817/http://www.shawnhargreaves.com/blogindex.html , archive-date=2019-06-30 {{cite book , title=Real-Time Systems Design and Analysis , chapter=Chapter 7.5.3, Binary Angular Measure , author-first=Phillip A. , author-last=LaPlante , date=2004 , website=www.globalspec.com , chapter-url=http://www.globalspec.com/reference/14722/160210/Chapter-7-5-3-Binary-Angular-Measure {{cite web , title=Doom 1993 code review - Section "Walls" , author-first=Fabien , author-last=Sanglard , date=2010-01-13 , website=fabiensanglard.net , url=http://fabiensanglard.net/doomIphone/doomClassicRenderer.php {{cite web , title=Hitachi HM55B Compass Module (#29123) , series=Parallax Digital Compass Sensor (#29123) , publisher= Parallax, Inc. , date=May 2005 , website=www.hobbyengineering.com , via=www.parallax.com , url=http://www.hobbyengineering.com/specs/PX-29123.pdf , url-status=dead , archive-url=https://web.archive.org/web/20110711172521/http://www.hobbyengineering.com/specs/PX-29123.pdf , archive-date=2011-07-11 Units of plane angle Binary arithmetic

Representation

Unsigned fraction of turn

Signed fraction of turn

See also

References