What is place value?

The full name of place value is place value notation. It is a commonly used notation method. It is a notation established according to the place value system. Place value notation refers to counting according to the place value system. Method, that is, the size of a number is represented by a set of sequential numbers. The size represented by each number depends on both its own value and its location.

Place value notation (positional notation), also known as place value notation, is a commonly used notation method and is established according to the place value system. The notation method is called place value notation. Decimal notation, binary notation, octal notation, etc. are all place value notation methods, while Roman notation does not belong to place value notation.

Place value notation refers to the method of counting according to the place value system, that is, the size of a number is represented by a set of sequential numbers. The size represented by each number depends on Its own value; in turn depends on its location.

The place value system, also known as the positional system and status system, was developed on the basis of the carry system. The so-called place value system means that if the same number is in different positions (digits), it will have different position values ​​(also called weights), so the values ​​represented are also different. In fact, it means that the position corresponds to one level. A certain multiple of "unit", such as 6, which means 6×1 in the ones place, 6×10 in the tens place, 6×100 in the hundreds place, etc. More strictly speaking, after selecting the base b of the carry system, the writing method (digital) of b numbers 0, 1, 2,..., b-1 is given. Therefore, any natural number N can be written using a certain A polynomial of b with these numbers as coefficients (can be repeated) is expressed:

Among them:

So In the "b carry value system" notation, we record N as:

Obviously, the same number is written in different positions, and the corresponding power of b The times are different, so the value represented by this number is also different. In addition, when we count in a specific b-carry value system, so as not to confuse it with the place-value system of other bases, we can omit the brackets for N and the base code b, and write directly:

This is exactly what people do in the commonly used decimal value system and the binary value system used in electronic computers.

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