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What is different when you say "Arithmetic Calculation" and "Calculation" in the context of the computer science?

The "arithmetic" in the former seems needless to me since all calculations are arithmetic.

Is there some meaning that is enhanced by adding "arithmetic" in this case?

Thank you in advance.

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  • $\begingroup$ Example: thunderstone.com/site/texisman/arithmetic_calculations.html $\endgroup$ – Jun Kyoto Nov 26 '14 at 8:15
  • $\begingroup$ Example 2: General-purpose computers have the amazing property that a single piece of hardware can do any computation imaginable. Before general-purpose computers existed, there were special-purpose computers for arithmetic calculations, which had to be manually reconfigured to carry out different calculations (Principles of Programming Languages cs.jhu.edu/~scott/pl/book/dist/book/book.pdf) $\endgroup$ – Jun Kyoto Nov 26 '14 at 8:19
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    $\begingroup$ You should include a page reference for your second example. There are 189 pages in the pdf $\endgroup$ – JoAnne Nov 26 '14 at 8:43
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    $\begingroup$ Not all calculations are arithmetic (that is, deal with numbers). You can do symbolic calculations with variables on a computer, using for example Mathematica. $\endgroup$ – painfulenglish Nov 26 '14 at 8:47
  • $\begingroup$ Even before symbolic calculations, you have things like sin(pi) which are trigonometric calculations. $\endgroup$ – Dan Bron Nov 26 '14 at 13:12
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"Arithmetic calculations" are those involving addition, subtraction, multiplication and division of numbers. eg (2+13)/5

There are also "algebraic calculations" eg Find y such that y + 2x = 13 and more.

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I'm sure my word processing program must do calculations, but since neither my input nor the results are expressed in numeric form, it hardly seems like arithmetic calculation. Is there an arithmetical operation called Insert, delete, or italicize? Of course, you could say these operations are reduced to arithmetical calculations, but in actuality, all calculations on a digital computer consist of combinations of and/or and nand/nor logic operations, some of which simulate arithmetic.

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What the computer does is move electric charges around, change magnetic state in some supports, read magnetic states, change some of this into light pulses for transmission, and many others similar microphysical manipulation.

Now it is up to you to interpret all that in whatever way you find convenient, and give it a name accordingly.

Ignoring the physics, and going up one level, you manipulate bits. A bit is just something that can have one of two possible states. All that matters is that you can distinguish them. You may call them 0 and 1, or true and false, or Yin and Yan, or black and red, or up and right.

Then there ways of manipulating them that encode more complex things. You can interpret a sequence of bits as a number, or as a letter, or as a fragment of a text, or as a painting, or as a symphony. Your choice, with appropriate encoding.

Then are you doing Arithmetic calculations, or composing music, orwriting/reading a novel, or solving an equation ...? It depends on the encoding and the manipulation.

But it is always calculation, in a sense, Calculation comes from the latin calculus : stone, as stones were initially used for counting (which is indeed arithmetic). But what survived is the idea of manipulating stones. And the name calculus is generally used to indicate some form of manipulation of entities supposed to represent something, usually the manipulation of symbol in the modern world.

So, yes, the computer does calculations. But that only means it is pushing bits around. And it may be for any purpose, since it is a universal way of representing information.

Note: The use of the word calculus alone to mean also diffential and integral calculus is more a linguistic accident. See: What are the justifications and historical reasons regarding the choice between the words 'calculus' and 'algebra'?

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