Number systems are classified into 2 main types — positional and non-positional. The specifics of those and others? What distinguishes positional number system non-positional from?

The content of the article

- That is a positional number system?
- The difference between positional and non-positional number system
- Comparison table

That is a positional number system?

The numeral system is characterized by the fact that the numbers in it depending on its position relative to the beginning of the number (when reading from left to right) will have a different effect. Right is the figure — the weaker it is. For example, the number 143 is the strongest digit is 1, because it represents hundred, next in strength to 4, because it denotes tens, the third power of the figure — 3, since it corresponds to the unit number.

Number systems considered to be positional in the world is used quite a lot. Among the most common — binary (used in programming), decimal (most common in daily life), octal, and hexadecimal (they are mainly used in engineering).

What is a non-positional number system?

The corresponding notation is characterized by the fact that the numbers in it don’t always share power depending on the position relative to the beginning of the number. The difference in their power, in principle, possible, but not always the rule.

For example, the Roman number XX (twenty) consists of two identical power numbers X, each of which represents ten. In turn, the number XV (fifteen) first digit is stronger because it has a decimal base, and the second is the unit number five.

In addition, non-positional number system, which uses Roman numerals, numbers to the left may be weaker. For example, the Roman numeral IV which is 4, is from the weaker to the left of I(one) and stronger, located to the right of V (five). Figure 4 is formed, therefore, by subtracting this figure from the more powerful.

to table of contents ↑the Difference between positional and non-positional number system

The main difference between positional numeral systems from non-positional is that in the first structure numbers consisting of more than one digit, all the digits are different in strength (generally stronger than those located to the left). In the second notation, this pattern is observed only in some cases. It is possible that the structure of the numbers will be the numbers with equal force. In this case, if the power of numbers different, not necessarily stronger will be located to the left, can be observed in reverse.

Defining the difference between positional and non-positional number system, identify the findings in the table.

to content ↑Comparative table

**Positional number system**

**Non-positional number system**

What is common between them?

In positional and non-positional systems are allowed different power figures

What is the difference between them?

In numbers consisting of 2 or more digits, all the digits are different in strength (generally stronger than those located to the left)

In numbers consisting of 2 digits or more, not always figures differ in strength (and if different, not always the stronger numbers are to the left)