Binary Degree (brad)

ComputingTraditional unit (still used in some regions)

One 256th of a turn (1.40625 degrees). A power-of-two angle used in computer graphics and old game engines so that wrapping is free.

1 binary degree = 0.00390625 turns (exactly).

1 binary degree = 1.40625 degrees

About the binary degree

Binary angular measurement stores an angle as an unsigned integer in which a full turn is 2ⁿ steps. In the 8-bit version a turn is 256 steps, so each step is 1.40625 degrees, and the values 0, 64, 128, and 192 mark 0, 90, 180, and 270 degrees. Wiktionary glosses the name brad, used for such units, as a binary radian.

The appeal is wraparound. Integer addition and subtraction overflow modulo 2ⁿ, so angles that differ by whole turns are automatically equivalent and no code is needed to reduce them to a standard range. With signed two's-complement values, the same bits cover −180 to +180 degrees. Real systems use longer words. The 16-bit furman, named for Alan T. Furman, who adapted the CORDIC method to 16-bit fixed-point arithmetic, is 1/65,536 of a turn, slightly less than 20 arcseconds, and GPS satellite ephemerides encode four orbital angles as 32-bit binary angles. Computer games are another common home for binary angles.

Sources: Wikipedia: Binary angular measurement; Wiktionary: brad

Binary Degree conversion chart

1 binary degree expressed in every other angle unit:

Unit1 binary degree
Degrees1.40625
Radians0.02454369261
Gradians1.5625
Turns0.00390625
Arcminutes84.375
Arcseconds5,062.5
Milliarcseconds5,062,500
Milliradians24.54369261
Right Angles0.015625
Octants0.03125
Sextants0.0234375
Hour Angles0.09375
Mils (NATO)25
Zodiac Signs0.046875
Compass Points0.125
Mils (Soviet)23.4375
Streck24.609375

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