|Spoiler Alert: This page contains spoilers. Read at your own risk.|
The Magic Calculation Area (魔法演算領域), or magic processor, is the part of the subconscious mind responsible for the use of magic.
After expansion, the expanded activation sequence is read by the magic processing area in the subconscious and variables such as coordinates, output, and duration are inputted, the result is inserted alongside the activation sequence and gives rise to the completed magic ritual.
This complete magic ritual is taken from the operations area of the subconscious and transferred to the lowest level of the conscious, the 'root', from the area between the conscious and the subconscious, the 'gate', whereupon it can be projected upon the outside world, as the magic ritual projects and targets 'information events' — in the study of modern magic, these are named 'Eidos' from Greek philosophy, and refers to the event where the information of the target is temporarily overwritten. 
In terms of function, the Magic Calculation Area's transforms the imagined reality into data and produces a Magic Sequence for the desired spell. Generally speaking, target coordinates, strength and ending requirements are all set as variables to be executed by the Magic Calculation Area; all other essentials are incorporated into the Activation Sequence, which is then sent to the Magic Calculation Area and translated into a Magic Sequence. In short, the target and power of the spell are determined by the Magician's mind whereas the nature of the spell is determined by the Activation Sequence.
Not much is understood about the Magic Calculation Area and despite many studies for no specific anatomic location dedicated purely for producing magic has been found. Furthermore, an individual has no way to determining the limits or the state of the Magic Calculation Area; in other words, a magician will not be able to tell he or she is over-stressing the Magic Calculation Area by overusing magic. This is highly problematic as overuse of powerful magic often drains life force to the point of death.
For example: Yotsuba Genzou
Still, there is enough information to know that each person's Magic Calculation Area is different, and this magic processor determines both the level of magic power and the magic specialty of the Magician.
There is a subgroup of magicians whose Magic Calculation Areas are dominated by one type of magic. They are known as Born-Specialized Magicians, or "BS Magicians". Unlike normal Magicians who can freely use all types of magic, BS Magicians can only use few types (sometimes as low as only one type) of magic. In exchange, they are capable of easily performing high level spells considered almost impossible for normal Magicians within those subsets of magic. Tatsuya is an example of a BS Magician who wields two types of magic: Decomposition and Regrowth.
The Yotsuba Family were involved in a series of experiences called the Artificial Magician Project. Yotsuba Miya, with the help of her Mental Design Interference, inserted an artificial Magic Calculation Area into the brains of several test subjects, including her son Tatsuya. The artificial processor in Tatsuya was highly inferior to the natural magic processor in all Magicians. The artificial magic processor was much slower and had much less interference strength than natural processors. Furthermore, as a side effect, Tatsuya ended up losing most of his strongest emotions and desires as a result of the procedure. It is also implied that Miya herself lost some of her emotions as well.
Still, the procedure allowed Tatsuya, who was completely unable to use any other forms of magic aside from Decomposition and Regrowth, to use other forms of magic. Also, an unexpected positive benefit is that due to Tatsuya's artificial Magic Calculation Area being located in his conscious mind, Tatsuya is able to see, understand, and memorize any Activation Sequence or Magic Sequence he sees. This has allowed him to take Flash Cast, a Yotsuba secret technique that allows Magicians to recall Activation Sequences from memory (allowing for casting speeds even faster than with a CAD) for basic spells (5 or fewer processes), to a new level. Tatsuya can not only use cast basic spells at a fast speed without a CAD like other members of his family, he can bypass recalling Activation Sequences and even constructing Magic Sequences entirely by storing images of Magic Sequences in his memory. Therefore, Tatsuya's Flash Cast is instantaneous. Considering that most combat spells fall within 5 or fewer processes, Tatsuya excels in combat.