Check the Active-Time and Charge Arithmetic

Ada re-derives this chapter’s own numbers step by step, at full precision

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Ada ADA · CALCULATION AUDIT

Check the Active-Time and Charge Arithmetic

On an FPU-less core a software floating-point multiply costs about 50 cycles, while the same work in fixed-point costs about 3 cycles. The chapter pushes both through a 16 MHz core drawing 1.5 mA while active — a 10,000-multiply burst and a 1,000-tap filter running at 100 samples/s — on the claim that fewer cycles simply mean a shorter awake window. This audit checks that step: do those cycle counts really turn into the active-time and charge savings the chapter claims?

Companion to the chapter Fixed-Point Arithmetic — every number here comes from that chapter.

Ada: The energy claim is only credible if the cycle counts become time and charge with the units carried through. These checks use only the chapter's existing 16 MHz clock, 1.5 mA active current, 10000-operation burst, 1000-tap filter, 100 samples/s rate, 50-cycle software-float cost, and 3-cycle fixed-point cost.

  • Burst active time: float 10000 x 50 / 16000000 = 0.03125 s = 31.25 ms; fixed 10000 x 3 / 16000000 = 0.001875 s = 1.875 ms.
  • Burst charge: float 1.5 mA x 0.03125 s = 0.046875 mA-s; fixed 1.5 mA x 0.001875 s = 0.0028125 mA-s.
  • Once-per-second saving: 0.046875 - 0.0028125 = 0.0440625 mA-s/s, so the average-current saving is 0.0440625 mA and the daily charge saving is 0.0440625 x 24 = 1.0575 mAh/day.
  • Filter duty cycle: float 1000 x 50 = 50000 cycles and 50000 / 16000000 = 3.125 ms/sample; fixed 1000 x 3 = 3000 cycles and 3000 / 16000000 = 0.1875 ms/sample.
  • Filter daily compute charge: at 100 samples/s, float duty is 100 x 3.125 ms = 0.3125 s/s, so 1.5 x 0.3125 x 24 = 11.25 mAh/day; fixed duty is 100 x 0.1875 ms = 0.01875 s/s, so 1.5 x 0.01875 x 24 = 0.675 mAh/day.

Every number above is taken from the chapter’s own material and re-derived step by step.