Binary computing

brief introduction

Binary is a number system widely used in computing technology . Binary data is used 0 and 1 A number represented by two numbers . Its cardinality is 2, The carry rule is “ On the two into one ”, The rule of borrowing is “ Borrow one for two ”, from 18 Leibniz, a German master of mathematical philosophy in the th century, found that . The current computer system is basically a binary system , Data is mainly stored in the form of complement in the computer . Because the logic of the circuit is only 0 and 1 Two states , there 0 and 1 It's not numerical 0 and 1,0 and 1 It means two different states ,0 Indicates low level ,1 High level . A computer is made up of innumerable logic circuits , adopt 0 and 1 The infinite number of bits and combinations to express information .

Java Built in conversion

stay Java There are several built-in methods to help us carry out various decimal conversions . As shown in the figure below （ With Integer Plastic surgery, for example ）：

 Binary system ：Integer.toBinaryString(int i)
 octal ：Integer.toOctalString(int i)
 Octagon ：Integer.toHexString(int i)

 Binary to decimal ：
    Integer.valueOf("0101",2)
    Integer.parseInt("11", 2)
 octal ：Integer.valueOf("376",8)
 Hexadecimal ：Integer.valueOf("FFFF",16)

Use Integer Class parseInt() Methods and valueOf() Methods can convert other base numbers to 10 Base number .

System.out.println("int Maximum positive number ：" + Integer.MAX_VALUE);
System.out.println("int The maximum positive binary representation ：" + Integer.toBinaryString(Integer.MAX_VALUE));
System.out.println("int Minimum negative number ：" + Integer.MIN_VALUE);
System.out.println("int The minimum negative number is binary ：" + Integer.toBinaryString(Integer.MIN_VALUE));

System.out.println(" Binary definition printing int The maximum number that can be represented ：" + 0b01111111_11111111_11111111_11111111);
System.out.println(" Binary definition printing int The smallest number that can be expressed ：" + 0b10000000_00000000_00000000_00000000);

System.out.println("43 Binary representation of ：" + Integer.toBinaryString(43));// The result omits the previous 0
System.out.println("-43 Binary representation of ：" + Integer.toBinaryString(-43));

// Underline is meaningless , Just for convenience , Can write at will 
int a = 0b00000000_00000000_00000000_00000000_00101011;//0b Represented as binary ,a The decimal equivalent of 43
int a1 = 0b101011;// It's also decimal 43, Just omit the above 0
System.out.println(" Print a Value ：" + a);
System.out.println(" Print a1 Value ：" + a1);

int b = 0b11111111_11111111_111111111_1010101;// Binary system 43 Add... In reverse 1, become -43, Underline is meaningless 
System.out.println(" Print b Value ：" + b);

int i = 0b00000001_00110010_01100111_10101101;// I wrote a decimal 24274861
System.out.println(" Print 10 It's binary i：" + i);
System.out.println(" Print is forced to short Of i：" + (short)i);
System.out.println(" Print short The binary representation of ：" + Integer.toBinaryString((short)i));

 result ：
int Maximum positive number ：2147483647
int The maximum positive binary representation ：1111111111111111111111111111111
int Minimum negative number ：-2147483648
int The minimum negative number is binary ：10000000000000000000000000000000
 Binary definition printing int The maximum number that can be represented ：2147483647
 Binary definition printing int The smallest number that can be expressed ：-2147483648
43 Binary representation of ：101011
-43 Binary representation of ：11111111111111111111111111010101
 Print a Value ：43
 Print a1 Value ：43
 Print b Value ：-43
 Print 10 It's binary i：20080557
 Print is forced to short Of i：26541
 Print short The binary representation of ：110011110101101

int To short when , Direct interception status 16 Bit conversion