From Real Time Systems Design And Analysis

7.5.3   Binary Angular Measure

Another type of scaled number is based on the property that adding 180o to any
angle is analogous to taking its two’s complement. This technique, called binary
angular measurement (BAM) works as follows. Consider the LSB of an n-bit
word to be 2n−1 · 180 degrees with the most significant bit (MSB) = 180 degrees.
The range of any angle θ represented this way is 0 ≤ θ ≤ 360 − 180 · 2-(n−1)
degrees. A 16-bit BAM word is shown in Figure 7.6. For more accuracy, BAM
can be extended to two more words. Each n-bit word has a maximum value of


with granularity


Consider the 16-bit BAM word:

 0000 0000 10100 110

Its binary angular measurement is 166 · 180o · 2−15 = 0.9118o.

Figure 7.6 A 16-bit binary angular measurement word [Laplante03c].

BAM can be added and subtracted together and multiplied and divided by
constants as if they were unsigned integers, and converted at the last stage to
produce floating-point results. It is easy to show that the overflow condition for
BAM numbers presents no problem as the angle simply wraps around to 0. BAM
is frequently used in navigation software, robotic control, and in conjunction with
digitizing imaging devices.


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