Difference between positional and non-positional number system.

Number systems are classified into 2 main types - positional and non-positional. What is the specificity of both?

What is the positional number system?

The considered number system is characterized by the fact that the numbers in it, depending on their position relative to the beginning of the number (when read from left to right), will have different strengths. The more to the right the number is located, the weaker it is. For example, in the number 143, the strongest digit is 1, since it denotes a hundred, then in strength - 4, since it denotes ten, the third most powerful digit is 3, since it corresponds to a single number.

Number systems considered positional are used in the world quite a lot. Among the most common are binary (used in programming), decimal (most common in everyday life), octal and hexadecimal (mostly used in engineering).

What is a non-positional number system?

The corresponding number system is characterized by the fact that the numbers in it are not always divided by strength, depending on the position relative to the beginning of the number. The difference in their strength is, in principle, possible, but not always the rule.

For example, the Roman number XX (twenty) consists of two equal numbers X, each of which denotes ten. In turn, in the number XV (fifteen), the first digit is stronger, since it corresponds to the decimal base, and the second to the single number five.

In addition, in a non-positional numeral system that uses Roman numerals, the number to the left may be weaker. For example, the Roman numeral IV, that is, 4, consists of a weaker one located to the left of I (one) and a stronger one located to the right of V (five). The number 4 is thus formed by subtracting the weaker number from the stronger one.

Comparison

The main difference between the positional number system and the non-positional one is that in the first number in the structure of a number consisting of more than one number, all numbers differ in strength (in the general case, those which are located to the left). In the second number system, this pattern is observed only in some cases. It is quite possible that numbers with the same strength will be present in the structure of the number. Moreover, if the strength of the numbers is different, it is not necessary that the stronger ones will be located to the left, the opposite situation can also be observed.

Having determined what is the difference between positional and non-positional number system, let us fix the conclusions in the table.

Table

Positional number system Non-positional number system
What do they have in common?
In positional and non-positional systems, the presence of numbers of different strengths is allowed
What is the difference between them?
In numbers that consist of 2 or more digits, all digits differ in strength (in general, those that are to the left are stronger)In numbers that consist of of 2 digits or more, the digits do not always differ in strength (and if they differ, the stronger digits are not always located to the left)
.