The tally system is simple. Only two symbols are needed to add and subtract values. Through the tally-mark system, symbol values are added together to obtain one number. There is no need to memorize a new symbol for every added value. The tally system plays a vital role in theoretical computer science and coding because of its ease of comprehension and use. Arbitrary-sized numbers and codes are expressed by the length of a binary numeral in computer science.
Almost anyone can draw a straight or diagonal line, which makes the numerical system universal. It can be taught fairly easily to young children and transferred across various regions despite language and cultural barriers. The tally mark system was the first numerical system of many indigenous cultures across the globe. It is often used by younger children as they become familiar with more complex counting systems.
Using the tally system for larger numbers becomes difficult and inefficient. Imagine writing thousands of strokes to represent a seven-digit figure. The thought of constructing that many tally marks, then conveying the message to others, can lead to miscommunication and even fatigue. Using tally marks and diagonal strokes after 50, therefore, is arduous and requires the addition of a more sophisticated numerical system.
Tallies and counts have difficulty modeling the process of division and multiplication, as well. There are no symbols, in fact, to express the processes. A mathematician could not transform a complex number or improper fractions into a tally mark, for example. The notion of zero and its involvement in upper-level mathematics cannot be converted, as well. The mathematician is limited to simple equations that involve addition, subtraction and numbers close to -- but never equivalent to -- zero.