[C language _ review _ learn Lesson 2] what is base system? How to convert between hexadecimals

Review before class :C What kind of language is a language ? A High-level language 、B Low level language 、 C Semiotic language 、 D assembly language , I believe everyone will not be wrong .

Catalog

Convert decimal to binary ：

Decimal processing :

Binary to decimal

8421 Patchwork

Convert decimal to octal

Octal to decimal ：

Binary to octal

Octal to binary

Binary to hexadecimal

Hexadecimal to octal

The ending egg ：

What is base ？ Our life is full of happiness everywhere , One day is 24 Hours 、 An hour is 60 minute 、 One minute is 60 second 、 There are... On a Monday 7 God ........ Have you ever heard of the word "half weight" ? That is to say, buying half a kilo of things means eight Liang , One kilo is sixteen Liang , full 16 In one digit, this is hexadecimal . I'll be a primary school teacher today to test you ,5+8 How much ( I'm not kidding you ) You would say equal to 13, Your answer is decimal, that is, full decimal one , In the computer, the numbers are in binary （ Only 1 and 0） What is stored is full binary , Of course, there are octal （ from 0 To 7）、 Hexadecimal （ from 0 To F） It's all similar , Octal full eight into one digit , Hexadecimal full hexadecimal into one digit ( Where hexadecimal 10 use A To express ,11-B、12-C、13-D、14-E、15-F).

Let's start asking The conversion between various hexadecimals

Hexadecimal said B Binary system   O or Q For octal 、D For decimal 、H For hexadecimal , You can also use corner markers （10）n Base number .

Convert decimal to binary ：

Integer processing ：

Convert decimal integers to binary integers. Convert decimal integers to binary integers using " except 2 Remainder , In reverse order " Law . The specific way is ： use 2 Divide decimal integers , You can get a quotient and a remainder ; Reuse 2 Get rid of business , And you get a quotient and a remainder , Do so , Until the quotient is less than 1 Until , Then take the remainder as the low significant bit of the binary number , The remainder is the high significant bit of the binary number , Put them in order .

Decimal processing :

Decimal decimal is converted to binary decimal by “ ride 2 Sort by integer ( Sort in positive order ). practice : Multiply by... Using decimal decimals 2, Then take the whole number , Until the decimal place is 0 until , Of course, some decimals can't be divided completely. We can keep them according to the accuracy .

Binary to decimal

The binary conversion bit decimal system can use the method of weighted expansion in addition

If it's a decimal , Just follow -1 Power 、-2 Calculate in the order of power .

8421 Patchwork

Personal skills ： We can use... When calculating binary conversion to decimal or decimal conversion to binary 8421 Patchwork .

8421 Patchwork : The bit on the left of binary is always twice the bit on the right , For example, binary 1 For decimal 1, Binary system 10 For decimal 2、 Binary system 100 For decimal 4、 Binary system 1000 For decimal 8, This is 8421 play . The left digit is twice as many as the adjacent right digit. We just need to remember the number above each digit to express the decimal system

128 64 32 16  8 4 2 1, In this way, we can easily express decimal . If decimal is converted to binary, then vice versa .

Convert decimal to octal

Converting decimal to octal is almost the same as converting decimal to binary , Ten to two yes " except 2 Remainder , In reverse order " Law . Ten to eight is divided by 8 Remainder , In reverse order .

The specific way is ： use 8 Divide decimal integers , You can get a quotient and a remainder ; Reuse 8 Get rid of business , And you get a quotient and a remainder , Do so , Until the quotient is less than 1 Until , Then take the remainder as the low significant bit of the binary number , The remainder is the high significant bit of the binary number , Put them in order .

Octal to decimal ：

The method of converting binary to decimal is the same , Expand by weight in the method of addition .

The conversion between decimal and hexadecimal is relatively simple

Ten to sixteen also use except 2 Remainder , In reverse order .

Sixteen to ten also uses the weighted expansion in addition method .

It should be noted that hexadecimal 10 use A Express , And so on ！

Binary to octal

Three bit binary can represent one bit octal , We can use 421 Dafa ( Because octal can represent 0-7 Three bit binary can represent 0-7）

Octal to binary

As can be seen from the above, three bits of binary represents one bit of octal , One octal represents three binary .

Binary to hexadecimal

A four bit binary can represent one hexadecimal bit , We can use 8421 Dafa ( Because hexadecimal can represent 0-15 That is to say 0-F A four bit binary can represent 0-15）

Hexadecimal to octal

In the same way as octal, one hexadecimal represents four binary .

Be careful ： Octal and hexadecimal cannot be converted directly , It needs to be converted to other base numbers first, and then converted

The ending egg ：

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