Hexadecimal conversion summary

Preface :
In learning the principles of computer composition chapter 2 - Operation method and arithmetic unit , Encountered a binary conversion problem , As a computer student , About binary conversion, we still need to understand clearly , I want to sum it up for a long time , Here are some calculation methods .
General content of the article : Decimal system , Binary system , Interval adjustment , Decimal conversion

Binary 、 octal 、 Hexadecimal to decimal

Integral part :

The fractional part :

Convert decimal to binary 、 octal 、 Hexadecimal :

Integral part :

Decimal to N Base number , With its number pair N Continuous surplus , Until the quotient is zero , Then arrange the remainder in reverse order , The number obtained is N Result after hexadecimal :

As shown in the figure :
Put the decimal number 36926 The process of converting to octal ：

I can see from the picture that , Decimal number 36926 The result of conversion to octal is 110076.

The fractional part :

Convert decimal to N Hexadecimal decimals are “ ride N integer , Sequential arrangement ” Law . The specific way is ：
Arrange the integer parts in order , First take the integer as N The high digit of a decimal , Take the integer taken out as the low-order number , So you get N Decimal number .

As shown in the figure :
Put the decimal number 0.930908203125 The process of converting to octal decimal ：

Decimal number 0.930908203125 The result of converting to octal decimal is 0.7345.

Binary and octal 、 Hexadecimal conversion :

octal :
Octal as a written form of binary , The base number is 8, Yes 0~7 common 8 A different number symbol , Count " Every eight enters one. ", because r=8=2 The third power of , So as long as the three digits in binary are grouped into a group, it is an octal digit , The conversion between the two is very convenient .

Hexadecimal :
Hexadecimal is also a common writing form of binary , The base number is 16,“ Every 16 to one ”. Each number is desirable 0~9,A,B,C,D,E,F Any one of , among A,B,C,D,E,F respectively 10 ~ 15 . because r=16=2 Of 4 Power , therefore 4 It is a binary number corresponding to a hexadecimal number .

Actually , Any conversion between hexadecimals can use the method mentioned above , But sometimes it's troublesome , Therefore, different methods are generally adopted for different hexadecimals . There is a very simple way to convert binary to octal and hexadecimal , vice versa .

1. Conversion between binary and octal integers
   When converting binary integers to octal integers , Convert every three binary digits into one octal digit , The order of operations is from low to high , If the high position is less than three digits, fill them with zeros . The following figure shows how to convert binary integers 1110111100 Convert to octal ：

As you can see from the diagram , Binary integer 1110111100 The result of conversion to octal is 1674.

When converting octal integers to binary integers , The idea is the opposite , Each octal digit is converted to three binary digits , The order of operations is also from low to high . The following figure shows how to convert octal integers 2743 Convert to binary ：

As you can see from the diagram , Octal integer 2743 The result of converting to binary is 10111100011.

2. Conversion between binary and hexadecimal integers
   When converting binary integers to hexadecimal integers , Convert every four binary digits to one hexadecimal digit , The order of operations is from low to high , If the high position is less than four digits, fill them with zeros . The following figure shows how to convert binary integers 10 1101 0101 1100 Convert to hex ：

As you can see from the diagram , Binary integer 10 1101 0101 1100 The result of conversion to hexadecimal is 2D5C.

When converting a hexadecimal integer to a binary integer , The idea is the opposite , Each hexadecimal digit is converted to four binary digits , The order of operations is also from low to high . The following figure shows how to convert hexadecimal integers A5D6 Convert to binary ：

As you can see from the diagram , Hexadecimal integer A5D6 The result of converting to binary is 1010 0101 1101 0110.

stay C In language programming , Binary system 、 octal 、 There is little conversion between hexadecimals , So here we only talk about the conversion of integers , It is enough for everyone to apply what they have learned . in addition , There is also very little direct conversion between octal and hexadecimal , We won't explain it here .

This article refers to the following documents , Predecessors summed up very well , In order to preserve , On the other hand, let yourself have a sorting process , I recorded this article .
Reference documents