Binary Fixed-Point Arithmetic

Extracting Signals from Noise and Other Distractions

- By Bob Japenga

Speed or precision? That's the basic decision involved in fixed-point versus floating-point arithmetic in computing. Bob looks deeply into the hows and whys of fixed-point arithmetic and explains why both speed and precision are possible with the right technique.

When I graduated from college, my first job was with Hamilton Standard (now Collins Aerospace). The part of the company that I worked for made strapdown inertial navigation systems (INS). In those days, most INS consisted of three or four gyroscopes and three or four accelerometers—one for each axis and, optionally, a fourth for error-checking places at 45 degrees to the coordinate system. In conventional systems, the inertial platform was mechanically gimbaled in such a way that the coordinate system remained fixed in space. The inertial platform was kept in a fixed orientation relative to their initial conditions when they were calibrated on the launch pad. The signals from the gyros and accelerometers fed the control system that used the gimbals to keep the inertial platform orientation fixed in space. With no movement of the initial inertial reference frame, the math for navigation was much simpler.

With the advent of computer power, it was possible for the guidance computer to perform the math for navigation with the gyros and accelerometers strapped down to the frame of the spacecraft. The math was intense. Our division’s INS were used on the Apollo Lunar Module backup guidance system (called the LM Abort Guidance System, Figure 1), the Viking Mars lander, and the Delta launch rocket. On the Apollo program, ours was the only strapdown INS.

I think I got the job because my senior project in aerospace engineering was helping a professor build a strapdown INS. I knew basically nothing about what it was or how it worked, but it was on my resume.