First, we have to convert all values to the same units. So, we still cannot operate directly with the respective values. Comparison, addition and subtractionĮven if consistent, units are not necessarily equal, because they can have different scaling factors. What we need to do for our structure, is to check if the exponents vectors match exactly. So, units are consistent only if they are of the same dimensions and with the same exponents. However, “m + mm” is possible, because both represent length and we can convert them to each other. The expression “m 2 + m 3” does not make sense as well, because you are trying to add area to volume. For example, “kg + m” does not make any sense, because both operands represent different physical dimensions. You can compare, add or subtract only values, which units are consistent. ![]() The first one will store the exponents for all seven physical dimensions (mass, length, time, current, temp, substance, luminosity) and the second one – the respective scaling factors: In the case of units, we will include a name and two vectors. It can contain multiple values of different types in a single variable. To store all this information, we need a special type of data called “structure”. Then, we have to define all possible operations like comparison, addition, subtraction, multiplication, division and exponentiation. We also need the corresponding scale factors, in order to allow for multiples. For that purpose, we need to store the information for how units are composed by the base ones. Full list of the available units is provided in the user manual:Īny software implementation must allow the units to be compared, converted and scaled. However, not all prefixes are commonly used for all units, and that is why they are not included in Calcpad. All possible prefixes are listed in the following tables: Name I this way, we can obtain multiples of both base and composite units. Other method to derive units is by adding prefixes. They can be always decomposed to their constituent units. By definition, force is mass × acceleration, so 1 N = 1 kg For example, forces are measured in Newtons (N). They correspond to the seven physical dimensions:Īll other units are derived from the above ones, using the respective laws of physics. ![]() There are only seven base units in the whole universe. But first, let’s make a brief overview of the theory basis. In this post, we will take a quick look inside Calcpad and see how units actually work.
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