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Representing and Expressing Measurement Data in Digital Systems

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Abstract

This article elaborates on a proposal for expressing measurement data in digital systems. Systems will deal with compact three-component expressions of data, comprising: an aspect, value and scale. The aspect and scale will be compactly encoded as unique digital identifiers, which can also serve as keys to access information held in central registers. A register-based way to provide legitimate conversion operations between different expressions of data is also envisaged.The proposal addresses known difficulties with digital representation of SI units and extends support to a range of measurement data that cannot be expressed in the SI. The notion of aspect is an extension of ‘quantity’ and ‘kind of quantity’, which are terms used in association with the SI. The idea of a scale combines a conventional measurement unit or reference with the notion of a particular mathematical structure for the expression of values, sometimes called a level of measurement.

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Notes

  1. Another possibility is to form a sequence of integer exponents, where the position of each exponent is associated with a base quantity. This is sometimes called a dimensional vector. Taking length as the first element and time as the second, we may encode x, t, v and a as: (1, 0), (0, 1), \((1,-1)\), and \((1,-2)\), respectively. Yet another approach appears in the SI Brochure, where a special notation for base quantities is adopted (\({\textsf{L}}\) for length and \({\textsf{T}}\) for time) and terms may be exponentiated and multiplied (so, \({\textsf{L}} {\textsf{T}}^{-1}\) represents speed) [16].

  2. The terminology of dimensions is often used to describe quantity and unit systems. However, the distinction between ‘dimension’ and ‘quantity’ is often unclear [8].

  3. Equations to convert between ITS-90 and thermodynamic temperature are available [24, 25].

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Acknowledgements

This work was funded by the New Zealand government. The author would like to thank Peter Saunders for careful reading of this manuscript and Annette Koo and Peter Saunders for useful discussions. The use-case discussed in “Use Case: Expressing Optical Spectroscopy Data” was suggested by Dr. Li-Lin Tay, at the Metrology Research Centre of the National Research Council Canada, following a public request for use cases involving digitalisation of measurement data (the request was on behalf of a task group set up by the International Committee for Weights and Measures—the CIPM TG-D-SI). The opinions expressed in the analysis of this case are the author’s alone.

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  1. Measurement Standards Laboratory of New Zealand, Callaghan Innovation, 69 Gracefield Road, Lower Hutt, 5010, New Zealand

    Blair Hall

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This article is part of the topical collection “Advances on Model-Driven Engineering and Software Development” guest edited by Luís Ferreira Pires and Slimane Hammoudi.

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Hall, B. Representing and Expressing Measurement Data in Digital Systems. SN COMPUT. SCI. 4, 120 (2023). https://doi.org/10.1007/s42979-022-01534-x

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