1.4 - fixed and floating point numbers

Catalog

One 、 Fixed-point number

1、 Definition

2、 Classification of fixed point numbers

Two 、 Floating point numbers

1、 understand

2、 Definition

3、 expression

4、 Floating point numbers are stored in the computer

5、 Understand the order code and mantissa

6、 Floating point operation

3、 ... and 、 Test method 1： Characteristics of fixed-point numbers and floating-point numbers

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One 、 Fixed-point number

1、 Definition

• A number whose decimal point is fixed , It is called fixed point number ;

2、 Classification of fixed point numbers

• Fixed point integers ： Agreed decimal point Fixed after the least significant digit ;

• Fixed point decimals ： Agreed decimal point Fixed after sign bit , Before the most significant digit ;

Two 、 Floating point numbers

1、 understand

• It is equivalent to scientific counting in life ; For example, in life 10 Base number 5000, It can be written in the following forms ;

• It can be seen from the picture that , The position of the decimal point can be changed constantly ; And the change of decimal point position , It does not affect the overall value of the expression ; This is floating point number ;

• So if you want to save 5000 The number of , You need to save both parts to be a complete number ;

2、 Definition

• The decimal point is not fixed , It can change ;

• A change in the position of the decimal point , It does not affect the size of the value ;

3、 expression

• M： mantissa ;

• R： base number ; Use the decimal system in life ,R Namely 10; Binary is used in computers ,R Namely 2;

• e： Index part ; In computer, it is called step code ;

4、 Floating point numbers are stored in the computer

• Because in the calculation set , The base number is 2, So there's no need to save ;

• Just save mantissa and exponent （ Order code ）, You can save a complete number ;

• So the expression format of floating point number in computer consists of two formats ： Order code + mantissa ;

5、 Understand the order code and mantissa

• Order code ： Determine the range of numerical representation , That is, the maximum number that this floating-point number can represent ;

• mantissa ： Determines the accuracy of the numerical representation ; The greater the mantissa, the more accurate the value is ;

Be careful ：

Because the fixed length of binary bits in the computer is agreed to represent a number , So increase the length of the order code or the length of the mantissa , It is bound to lead to changes in another part ;

6、 Floating point operation

（1） Operation steps

（2） Antithetic order ： Let the order codes of numbers be the same ;

• for example , A number represented by scientific notation minus an integer B, It is not possible to subtract integers directly from the base of scientific counting , It is necessary to adjust the two numbers to the format of the same index before operation ;

（3） Mantissa calculation

（4） Result formatting

• Convert the result into the corresponding format as required .

3、 ... and 、 Test method 1： Characteristics of fixed-point numbers and floating-point numbers