Each digital symbol is multiplied by the corresponding bit weight and added to represent the size of the number, and "bit" represents the size of the multiple of the digital symbol. Because there are infinitely many numbers, if you want to use a limited number of numbers to represent an infinite number of possible numbers, you need to use decimal, and decimal and digits must be connected to make sense. The so-called "decimal system" means that the number symbol returns to zero at the top and advances to the high position. For example, the numbers we use every day are decimal numbers, and the so-called decimal numbers are all decimal ones.
In addition to the commonly used decimal numbers, there are computer binary, octal and hexadecimal which are convenient to represent the digital state of computers, as well as clock decimal, hexadecimal (the clock cycles once every 12 hours, and 24 hours constitute a day) and hexadecimal (1 minute =60 seconds, 1 hour =
Second, the concept of position.
In our most commonly used decimal system, the values represented by different digits have different levels, such as single digits, tens digits, hundreds digits, thousands digits and tens digits. Twenty thousand is two tens of thousands. By multiplying symbols and bits and adding bits, large numbers can be conveniently represented.
People who have a math level above primary school think this is easy to understand, but in ancient times, there was no way to invent "bit"! For example, in ancient Rome, seven Roman letters were used as numbers:
ⅰ( 1)、X( 10)、C( 100)、M( 1000)、V(5)、L(50)、D(500)、
Put the small number to the right of the big number, indicating the number obtained by adding these numbers, such as ⅷ = 8, =12; If the decimal (limited to I, X, C) is on the left of a large number, it means the number obtained by reducing the number of large numbers, such as Ⅳ = 4, Ⅶ = 9; Draw a horizontal line above a number, indicating that the number has increased by 1 000 times, as shown in.
If you want to represent 3476 (Arabic numerals), use ancient Roman numerals to represent it as: MMMCDLXXVI, and use our traditional representation in China as: 3476, which is less than the ancient Roman representation and easier to read!
Our ancestors in China used "characters" to determine the "bits" of numbers, but ancient Rome did not separate bits from numbers, which brought trouble to representing large numbers.
At present, we use the method of "floating position" to write commonly used Arabic numerals. It is convenient to express very large numbers and decimals by using the previous method with large digits.
Include hours, minutes, seconds, etc. It is also a bit in a broad sense. The benchmark representing the size of a numerical value or quantity is the meaning and concept of "bit". The numerical value on a bit (such as decimal 0~9) can only be multiplied by a certain bit to determine the size it represents.
Third, the decimal system in mathematics
In mathematics, besides the decimal system commonly used by ordinary people, there are also binary and hexadecimal systems commonly used in computer, electronics, information and other scientific fields. The decimal system is represented by nine "symbols": 0, 1, 2, 3, 4, 5, 6, 7, 8, 9***, and the decimal point "."is different from the former, but it is also a necessary part of the decimal. In the binary system, only 0 and 1 are used to represent numbers, and the decimal point "."can also be added to represent decimals.
Because there are 16 symbols in hexadecimal to represent the numerical value of each bit, we add "A = 10, B= 1 1, C= 12, D = 1" to the decimal number.
How are the numbers expressed in different binary systems calculated? As shown in the following figure: (Generally, basic understanding of high school mathematics is required)
Hexadecimal and binary are closely related, because computers basically use binary to represent numerical values, but because binary is inconvenient to read and write, it is very convenient to "represent" binary with hexadecimal, as shown in the following figure.
1 hexadecimal symbol corresponds to 4 binary symbols, which can be connected together. So for scientific engineers, as long as they remember the symbols of hexadecimal and binary, binary and hexadecimal are very easy to convert each other.
4. How to directly convert numbers in different decimals?
In the third section, we have introduced how to convert other decimal numbers into decimal numbers, as long as you add the number symbol × the bit weight corresponding to each bit. The following figure shows an example of converting decimal numbers into binary numbers and hexadecimal numbers:
For other systems, the conversion principle is the same, so it is not commonly used, so I will not demonstrate it here.