Representing quantities and units in digital systems

Abstract

Systems of quantities and units were introduced by Maxwell in the late 19th century. However, adapting these ideas for use in modern digital systems has proven difficult. We present an interpretation of units and dimensions that clarifies the main reasons for this difficulty. We then suggest how a central register of metrological information would support quantities and units. Digital systems that handle data may refer to this register to express measured quantities. This will resolve problems with ambiguity, delineate meaningful usage, and allow data to be rendered in familiar formats to people without compromising the underlying information content. We call the proposal a digital metrology layer, or M-layer. An M-layer expression has three components: 1) the kind of quantity, or aspect; 2) the value; and 3) the scale. The aspect and scale components appear in an expression as succinct references to information held in the central digital register. The M-layer notion of scale combines a measurement unit, or other type of reference, with information about the level of measurement. The notion of aspect extends the idea of kind of quantity, which plays an important role in unit systems.

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