Bits and Information & integer notes

Basic knowledge of machine operation ：

1、 Binary system because ：a. Switch circuit characteristics ;b. The operation mode is simple ;c. Anti interference ;d. Matching Boolean algebra , And become the number system used by electronic computers .

Binary system 、 Hexadecimal 、 The conversion between the three decimal systems （ Bottom weight formula 、 Power splicing and so on ）, Hexadecimal addition and subtraction operations will be applied to memory address operations .

2、 Bit operation and logic operation ：

Note that bit operations expand parameters into bit vectors , Then operate by bit , The result is still a bit vector ; Logical operations only judge whether operands are non 0 Only judge whether it is not 0, by 0 Then it's false , Not 0 It is true . The result is either 0x00（ false ）, Either for 0x01（ really ）.

3、 Shift operation ：

  Shift operation can be realized very conveniently 2 Multiplication and division to the power of （ But this is not the only use of displacement ）. Logical left shift and arithmetic left shift are complemented on the right after the shift 0; Logical shift right , Left complement 0,; Logical shift right , On the left is the sign bit （ Nonnegative complement 0, Negative numbers make up 1）.

4、 Memory Is a linear combination of bytes , Memory is addressed by bytes , That is, one address corresponds to one byte , The storage of data in memory follows two patterns （ Big end method and small end method ）.

Small end method keyword ： Small 、 low 、 low （ The small endian method is to put the low order byte on the low order of the data ）; Or a pithy formula ： high and low （ High data to high address , Low data to low address ）

Signed numbers and their relationship with unsigned numbers ：

1、 Complement code ： The definition of complement is to take the first place as the sign bit and turn it into a negative weight , So as to realize the expression of negative numbers ; In essence , The complement is to set the highest digit to 1 Binary number of “ translation ”2w To negative half axis , A negative number used to express a complementary relationship with it .eg：w=4, 1010 Originally +10, Changing to complement means and +10 stay 24=16 Complementary in scope -6.

2、 The value and range of complement ： Use the complement value box , Or use complementary relationships , Or directly use the bottom weight formula that defines the complement , Find the value of complement . By observing the value range of complement, we can find , Different from the original code and inverse code , There is only one complement 0, It is convenient to confirm the calculation results . Also because of being alone 0 The existence of , The range of complement is asymmetric .w Signed number of bits （ Complement code ） The range of phi is zero ：-2w-1—2w-1-1.

3、 Ask for a complement Methods ： To reverse directly +1;|X| First from the right 1 And its right side remains unchanged , The left side is reversed .( The sign bit is also reversed )

4、 Mutual mapping and transformation ：

Signed numbers and unsigned numbers are mapped one by one , The key point of mapping , It is also the only connection point , Is their binary expression . A binary vector , It can be explained as signed number and unsigned number respectively , Between the two numbers explained separately , If it is a non negative number, they are the same （ The complement of a nonnegative number makes itself ）, If one of them is negative, the difference between the two is 2w. stay C In language, the two can be forcibly converted to each other .