BCD code Baidu Encyclopedia

BCD code （Binary-Coded Decimal‎）, use 4 position Binary number To express 1 position Decimal number Medium 0~9 this 10 Number , It's a binary form of digital coding , use Binary coded decimal system Code .BCD This form of coding uses four bits to store a decimal number , send Binary system and Decimal system The conversion between can be carried out quickly . This coding technique is most commonly used in the design of accounting systems , Because the accounting system often needs to accurately calculate a long string of numbers . Compared with the general floating-point type Notation , use BCD code , The accuracy of the values can be preserved , It can also avoid the time spent by the computer in floating-point operation . Besides , For other calculations that require high accuracy ,BCD Coding is also very common .

brief introduction

BCD Code is also called binary code decimal number ,BCD Codes can be divided into Right code and Unauthorized code Two types of . among , Common have the right to BCD The code has 8421 code 、2421 code 、5421 code , Have no right BCD There are more than yards 3 code 、 more than 3 Cyclic code 、 Gray code .8421BCD Code is the most basic and commonly used BCD code , It is similar to a four bit natural binary code , Your weight is 8、4、2、1, So it's called right BCD code .5421BCD Code and 2421BCD Both codes are entitled codes , Their weights from high to low are 5、4、2、1 and 2、4、2、1. more than 3 Code is by 8421 Code plus 3 After the formation of , It's a kind of “ Yes 9 Self complement of ”. more than 3 Cyclic code is a kind of variable weight code , Each bit does not represent a fixed value in different codes , The main feature is that there is only one bit of state difference between two adjacent codes . Gray code （ Also called cyclic code ） By Bell Laboratories FrankGray stay 1940 Put forward in , be used for PCM Method to prevent errors when transmitting signals . Gray code is a set of numbers , It is unauthorized code , Its two adjacent codes have only one different value . more than 3 The cyclic code is taken 4 Ten codes in the bit gray code , It also has the characteristics of adjacency [1] .

Category

8421

8421 BCD Code is the most basic and commonly used BCD code , It is similar to a four bit natural binary code , Everyone A weight by 8、4、2、1, So it's called right BCD code . And four bit natural binary code is different , It only uses the first four bit binary code 10 Group code , The box 0000~1001 Respectively represents its corresponding Decimal number , The remaining six sets of codes are not used .

5421 and 2421

5421 BCD Code and 2421 BCD Code is entitled BCD code , Their weights from high to low are 5、4、2、1 and 2、4、2、1. These two kinds of rights BCD In code , There are two kinds of decimal digits weighting Method , for example ,5421 BCD The number in the code 5, You can use 1000 Express , It can also be used. 0101 Express ;2421 BCD The number in the code 6, You can use 1100 Express , It can also be used. 0110 Express . This explanation 5421 BCD Code and 2421 BCD The coding scheme of code is not unique , surface 1-2 Only one coding scheme is listed .

The above table 2421 BCD The code 10 Among the numbers ,0 and 9、1 and 8、2 and 7、3 and 6、4 and 5 Exactly one of the corresponding bits of the code is 0 when , The other is 1. It's called 0 and 9、1 and 8 Each other Inverse code .

more than 3 code

more than 3 Code is 8421 BCD Add... To each code group of the code 3(0011) Formed . Commonly used in BCD In the operation circuit of code .

more than 3 Cyclic code

more than 3 Cyclic code Is the unauthorized code , That is... In each code 1 and 0 There is no exact weight , The whole code directly represents a value . The main advantage is that there is only one bit change in adjacent codes , The generation of transition code is avoided “ noise ”.

Gray code

Gray code （ Gray code ） Also known as Cyclic code , In the coding of a set of numbers , If the code of any two adjacent numbers is only one binary number different [2] .Gray There are many coding schemes , Typical Gray The code is shown in the following table . It can be seen from the table that , This code has the characteristics of unit distance code , Another feature is that it has reflective properties , That is, as shown in the table Axis of symmetry As a boundary , In addition to the highest complementary reflection , The remaining low order numbers are mirrored symmetrically along the axis of symmetry . Using this reflection characteristic, it is convenient to form Gray code .

Encoding mode

Most commonly used BCD code , Is the use of "0" to "9" The binary code of these ten values . This kind of coding , It's called “8421 code ”（ What we say everyday BCD Code mostly refers to 8421BCD Code form ）. in addition to , Corresponding to different needs , Everyone has also developed different coding methods , To adapt to different needs . These codes , It can be roughly divided into weighted code and unauthorized code ： Entitled BCD code , Such as ：8421( The most commonly used )、2421、5421…

Have no right BCD code , Such as ： more than 3 code 、 Gray code …（ Be careful ： Gray code is not BCD code ） Here are three common BCD Coding comparison .

Decimal number 8421-BCD code more than 3-BCD code 2421-A code

(M10) DCBA C3C2C1C0 a3a2a1a0

0 - 0 0 0 0 / 0 0 1 1 / 0 0 0 0

1 - 0 0 0 1 / 0 1 0 0 / 0 0 0 1

2 - 0 0 1 0 / 0 1 0 1 / 0 0 1 0

3 - 0 0 1 1 / 0 1 1 0 / 0 0 1 1

4 - 0 1 0 0 / 0 1 1 1 / 0 1 0 0

5 - 0 1 0 1 / 1 0 0 0 / 1 0 1 1

6 - 0 1 1 0 / 1 0 0 1 / 1 1 0 0

7 - 0 1 1 1 / 1 0 1 0 / 1 1 0 1

8 - 1 0 0 0 / 1 0 1 1 / 1 1 1 0

9 - 1 0 0 1 / 1 1 0 0 / 1 1 1 1

Commonly used BCD code

Decimal number	8421 code	5421 code	2421 code	more than 3 code	more than 3 Cyclic code
0	0000	0000	0000	0011	0010
1	0001	0001	0001	0100	0110
2	0010	0010	0010	0101	0111
3	0011	0011	0011	0110	0101
4	0100	0100	0100	0111	0100
5	0101	1000	1011	1000	1100
6	0110	1001	1100	1001	1101
7	0111	1010	1101	1010	1111
8	1000	1011	1110	1011	1110
9	1001	1100	1111	1100	1010

give an example

A binary unsigned number 11101010, Convert to three digits Uncompressed BCD Count , Press hundreds 、 Ten Bit and The order of bits indicates , Should be C.

A.00000001 / 00000011 / 00000111 　B. 00000011 / 00000001 / 00000111

C.00000010 / 00000011 / 00000100 　D. 00000011 / 00000001 / 00001001

Explain :(1)11101010 Convert to Decimal system :234

(2) Press hundreds 、 The order of ten bits and one bit indicates , Should be C.

Note appended ： Compress BCD code And Uncompressed BCD code The difference between —— Compress BCD Every bit of the code uses 4 Bit binary representation , A byte represents two bits Decimal number . for example 10010110B Represents a decimal number 96D; Uncompressed BCD code use 1 Bytes represent a decimal number , The senior four are always 0000, low 4 Bit 0000_{1001 Express 0}9. for example 00001000B Represents a decimal number 8.

BCD Algorithm of code

BCD Operation rules of code ：BCD The code is a decimal number , When the arithmetic unit adds and subtracts the data , They are processed according to binary operation rules . such , When will BCD When the code is transmitted to the arithmetic unit for operation , The result needs to be corrected . The revised rule is ： When two BCD Code addition , If the sum is equal to or less than 1001( namely Decimal number 9), No correction is required ; If the sum is 1010 To 1111( Hexadecimal number 0AH～0FH) Between , You need to add 6 Amendment ; If you add , Standard produces carry , Also need to add 6 Amendment . And the reason for that is , Press the machine Binary system Add up , therefore 4 position Binary number When adding , Is in accordance with the “ Every 16 to one ” The principle of operation , And in essence 2 Add decimal numbers , You should press “ Dot into one ” The principles of add ,16 And 10 Difference between 6, So when and exceed 9 There may be rounding , All need to be added 6 Amendment . Here's an example .

【 example 1.3】 Need to fix BCD Examples of code operation values .

(1) Calculation 5+8;(2) Calculation 8+8

Explain ：(1) take 5 and 8 With 8421 BCD Input machine , Then the operation is as follows ：

0 1 0 1

+) 1 0 0 0

1 1 0 1 The result is greater than 9

+) 0 1 1 0 Add 6 correct

1 0 0 1 1 namely 13 Of BCD code

The result is 0011, namely Decimal number 3, It also generates carry .5+8=13, The conclusion is correct .

(2) take 8 With 8421 BCD Input machine , Then the operation is as follows ：

1 0 0 0

+）1 0 0 0

1 0 0 0 0 Generating carry

+）0 1 1 0 Add 6 correct

1 0 1 1 0 16 Of BCD code

The result is 0110, namely Decimal system Of 6, And generate carry .8+8=16, The conclusion is correct .

Microcomputer principle code ： （AL=BCD 5,BL=BCD 8） set up AH=0, be

ADD AL,BL

AAA

The result is AX=0103H, Represents uncompressed Decimal number ,CF=1,AF=1,AH=1,AL=3

Use AAA Instructions , It is not necessary to mask the high half byte , Just execute immediately after adding AAA Instructions , Then you can be in AX Get a correct uncompressed decimal number in