C + + signed and unsigned number conversions

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1. Example:

Today we are doing a question about the conversion of signed numbers and unsigned numbers to their left/right shifts, and the principle of transformation between them and the principle of displacement is getting a big head. I really regret that I did not seriously study the principle of computer composition/computer operating system and other basic computer courses. The following is I based on the relevant knowledge review and collation of materials, if there are and so on the similarities of articles, please do not be offended. Also hope to see this article comrades can have something to gain it.

1#include <cstdio>2#include <iostream>3 using namespacestd;4 5 intMain ()6 {7Unsigned Short intUI;8Signed Short intsi;9UI = (unsigned Short int)0x8000u;TenSi = (Signed Short int)0x8000; Oneprintf"UI =%u\n", UI); Aprintf"si =%d\n", si); -UI = Ui>>1; -Si = si>>1; theprintf"UI =%u\n", UI); -printf"si =%d\n", si); -cout<<"------------------------------"<<Endl; -  +UI = (unsigned Short int)0x8000u; -Si = (Signed Short int)0x8000; +printf"%u\n", UI); Aprintf"%d\n", si); atUI = ((Signed Short int) ui>>1);//Shift first, then type conversion -Si = ((unsigned Short int) si>>1); -printf"%u\n", UI); -printf"%d\n", si); -cout<<"------------------------------"<<Endl; -  inUI = (unsigned Short int)0x8000u; -Si = (Signed Short int)0x8000; toprintf"%u\n", UI); +printf"%d\n", si); -UI = ui<<1; theSi = si<<1; *printf"%u\n", UI); $printf"%d\n", si);Panax Notoginsengcout<<"-------------------------------"<<Endl; -  theUI = (unsigned Short int)0x8000u; +Si = (Signed Short int)0x8000; Aprintf"%u\n", UI); theprintf"%d\n", si); +UI = ((Signed Short int) ui<<1); -Si = ((unsigned Short int) si<<1); $printf"%u\n", UI); $printf"%d\n", si); -     return 0; -}

Run results

2. Concept
In a computer, you can differentiate the number of positive and negative types, become a signed number (signed), a number with no positive or negative type (only an integer type), and become an unsigned number (unsigned). To be concise, unsigned means that all of its digits are used to denote the size of a numeric value, with the number of symbols in addition to the highest digits representing the positive and negative values (0 for positive numbers; 1 for negative numbers) and others to indicate the size of the values. For example: Ten mechanism number positive 2,552 binary expression form: 1111 1111

Ten mechanism number negative-12 binary expression form: 1111 1111

Visible-1 of the binary's highest bit is red 1, but why is it expressed in 1111 1111 instead of 1000 0001? This is about any number that is stored in the computer in the form of a complement. The following will be introduced, not in detail in this first.

3. Storage Range

As can be seen from the previous introduction, since the highest bit of the signed number is used as the sign bit, it is able to express a maximum value smaller than the maximum number of unsigned numbers can be expressed. Let me give you an example to illustrate this:

Unsigned number: 1111 11,110 binary Value: 255

Number of symbols: 0111 11,110 binary Value: 127

This is a question that one might ask: Can the number of symbols be expressed in a range less than the range of values that an unsigned number can express?

Oh, the answer is negative! Although the ability of the signed number to express the maximum is weakened, it can express negative values. The number of negative numbers can compensate for their shortcomings. Let's compare:

The expression value range of the unsigned number of a byte is: [0,255]

The value range of the symbolic number of a byte is: [ -128,0], [0,127]

It can be seen that they all represent 256 numbers.

4. Various codes (original code/inverse code/complement)

Some people may think that the "1" (double-byte) expression in the computer is 1000 0000 0000 0001, but it is not. The computer is expressed in its complement form, that is, "1" (double-byte) expression is 1111 1111 1111 1111.

Let's talk about the concept of various codes.

Original code: An integer, converted to a binary number according to the absolute value, the highest bit is the sign bit.

Anti-code: the original code in addition to the highest bit (sign bit), the rest of you bitwise reverse, the resulting binary code. The inverse code of the positive number is the original code.

Complement: Counter code the lowest bit plus 1 is the complement.

The complement of the negative number of the method to explain, first get its anti-code, and then the anti-code plus 1 can. Some of the great gods according to their original code, close eyes to get, this ability needs to cultivate a bit ah.

Then some people may say, why should we introduce the form of complement? Storing directly in the original code is not much easier? Hey, remember, some things are not you want to save the hassle of convenient. Well, let's enjoy the strength of the complement.

The advantages of a computer with the symbol number in the complement representation:

The conversion between the complement of 1 negative numbers and the complement of the corresponding positive numbers can be accomplished by using the same method-the complement operation, which simplifies the hardware. 2 You can turn subtraction into addition, so that subtraction can be calculated with the adder. If the highest bit (sign bit) has a carry, the carry is discarded when the number of 32 complements is summed.

Mental arithmetic to complement (the big God to find the algorithm):

From the lowest bit to the first found 1 is the same, the sign bit is unchanged, between the "negation" (0 change 1;1 0).

Original code: 1010 1001 Complement: 1101 0111.

5. The mutual conversion between signed number and unsigned number

The bit pattern does not change when casting between unsigned integers and signed integers.

When a signed number is converted to an unsigned number, negative numbers are converted to large positive numbers, which is equivalent to adding 2 N to the original value, while positive numbers remain unchanged.

When an unsigned number is converted to a signed number, the original value is maintained for the small number, and the large number is converted to negative numbers, which is equal to the original value minus 2 of the n-th square.

When there are signed and unsigned number types in an expression, all operations are automatically converted to unsigned types. The operation precedence of the visible unsigned number is higher than the signed number.

unsignedint=;  Signedint=-;         

The result is b>a.

6. Convert your meal

The conversion of a signed number

Original type	Target type	Conversion method
Char	Short	Symbol bit extension
Char	Long	Symbol bit extension
Char	unsigned char	The highest sign bit loses its bit meaning and becomes a data bit
Char	unsigned short	The sign bit expands to short, then goes from short to unsigned short
Char	unsigned long	The sign bit extends to long, and then from long to unsigned long
Char	Float	The sign bit extends to long, then goes from long to float
Char	Double	The sign bit extends to long, and then from long to double
Char	Long double	The sign bit extends to long, and then from long to long double
Short	Char	Keep Low byte
Short	Long	Symbol bit extension
Short	unsigned char	Keep Low byte
Short	unsigned short	Up to loss of meaning, to data bits
Short	unsigned long	The sign bit extends to long, and then goes from long to unsigned long
Short	Float	The sign bit extends to long, then goes from long to float
Short	Double	The sign bit extends to long, and then goes from long to double
Short	Long double	The sign bit extends to long, and then from long to long double
Long	Char	Keep Low byte
Long	Short	Keep Low byte
Long	unsigned char	Keep Low byte
Long	unsigned short	Keep Low byte
Long	unsigned long	Up to loss of meaning, to data bits
Long	Float	Using a single-precision floating-point number indicates a possible loss of precision
Long	Double	Using a single-precision floating-point number indicates a possible loss of precision
Long	Long double	Using a single-precision floating-point number indicates a possible loss of precision

The conversion of unsigned numbers

Original type	Target type	Conversion method
unsigned char	Char	Highest as symbol bit
unsigned char	Short	0 extensions
unsigned char	Long	0 extensions
unsigned char	unsigned short	0 extensions
unsigned char	unsigned long	0 extensions
unsigned char	Float	Convert to long, then convert from long to float
unsigned char	Double	Convert to long, and then convert from long to double
unsigned char	Long double	Convert to long, and then convert from long to long double
unsigned short	Char	Keep Low byte
unsigned short	Short	Highest as symbol bit
unsigned short	Long	0 extensions
unsigned short	unsigned char	Keep Low byte
unsigned short	unsigned long	0 extensions
unsigned short	Float	Convert to long, then convert from long to float
unsigned short	Double	Convert to long, and then convert from long to double
unsigned long	Long double	Convert to long, and then convert from long to long double
unsigned long	Char	Keep Low byte
unsigned long	Short	Keep Low byte
unsigned long	Long	Highest bit as sign bit
unsigned long	unsigned char	Keep Low byte
unsigned long	unsigned short	Keep Low byte
unsigned long	Float	Convert to long, then convert from long to float
unsigned long	Double	Convert directly to Double
unsigned long	Long double	Convert to long, and then convert from long to long double

7. Bytes of various data types

Under 32-bit platforms:

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C + + signed and unsigned number conversions