What a Reading Costs, From 4 Bytes to 530 Megabits

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

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Ada ADA · CALCULATION AUDIT

What a Reading Costs, From 4 Bytes to 530 Megabits

The chapter spans a huge range of byte costs: a raw-binary reading of just 4 bytes, mono audio at 224 kbps, a single RGB still at about 3 MB, and a 720p RGB stream of 531 Mbps. All of them answer one question — how many bytes does the data actually cost? This audit verifies every figure, tracing what a reading really costs, from a 4-byte record to a half-gigabit video stream.

Companion to the chapter Data Encoding and Codecs — every number here comes from that chapter.

Ada: This chapter spans two budgets that look unrelated – how many readings fit in a 51-byte uplink, and why raw media forces a codec – but both answer the same question: how many bytes does the data actually cost? Let me verify every figure from the chapter’s own encodings and sample rates.

  • Readings per 51-byte payload: JSON at ~32 bytes fits 51 / 32 = 1 reading; CBOR at ~18 fits 51 / 18 = 2 (36 bytes used, 15 to spare); raw binary at ~4 fits 51 / 4 = 12 readings – a 12x span for the same measurement.
  • Mono audio: 16000 samples/s x 14 bits = 224000 bps = 224 kbps, exactly as stated, before any header.
  • CD-quality stereo: 44100 x 16 bits x 2 channels = 1411200 bps = 1.41 Mbps – the chapter’s ~1.4 Mbps.
  • One RGB still: 1024 x 1024 x 3 bytes = 3145728 bytes = 3.15 MB – the chapter’s ~3 MB.
  • 720p RGB at 24 fps: 1280 x 720 x 3 bytes x 24 frames x 8 bits = 530841600 bps = 531 Mbps, confirming “above 500 Mbps.”

The audit conclusion is a set of ratios worth internalizing: the raw video stream (531 Mbps) is about 2370x the raw audio stream (224 kbps), and the raw-binary reading (4 bytes on the wire) is 12x denser than the JSON one (32 bytes). The design meaning is that encoding choice is not cosmetic – it moves the byte budget by one to three orders of magnitude, so “which fields and which codec” is a release decision that determines whether a link, a battery, or a storage plan is even feasible, not a formatting preference.

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