Introduction to BCD codes and code conversion between decimal numbers

1. Introduction to BCD code

BCD code (Binary-Coded Decimal‎) is called binary code, which uses 4-digit binary numbers to represent the 10 digits 0~9 in the 1-digit decimal number. It is the most commonly used type of decimal code.

In this encoding method, each "1" of the binary code represents a fixed value. Add up the binary numbers represented by each "1" to get the decimal number it represents. Because each "1" in the code represents the numbers "8", "4", "2" and "1" from left to right, it is named 8421 code. The decimal number represented by each "1" is called the weight of this bit. Because the weight of each bit is fixed, the 8421 code is a constant weight code.

BCD codes can be divided into two categories: authorized codes and unauthorized codes:

1. The authorized BCD codes include 8421 code, 2421 code and 5421 code, among which 8421 code is the most commonly used BCD code.
2. Unauthorized BCD codes include remainder 3 codes, remainder 3 cyclic codes, etc.

By analogy with 8421BCD code, we can get 5421 code and 2421 code.

It can be seen that the 8421 code, the 5241 code and the 2421 code are all decimal codes, but the weight of the rightmost digit is different.

In the picture, you can see that the BCD codes of several digits from 0 to 9 are converted in the normal binary form, and the BCD codes starting from ten start to be different .

BCD code: represents a number using four binary digits as one unit. For example: the BCD code of the decimal number 10 is 0001 0000; obviously the last four digits of 0000 represent the ones digit of the decimal system, and 0001 is the tens digit. The same goes for converting hexadecimal to BCD.

2. Conversion between BCD code and decimal system

 Convert 8421 code to decimal number

unsigned char bcd_to_hex(unsigned char data)
{
    unsigned char temp;

    temp = ((data>>4)*10 + (data&0x0f));
    return temp;
}

Convert decimal number to 8421 code

unsigned char hex_to_bcd(unsigned char data)
{
    unsigned char temp;

    temp = (((data/10)<<4) + (data%10));
    return temp;
}

Attachment: The conversion relationship between several code systems

Decimal	binary	8421 codes	5421 codes	2421 codes	Three more yards	remainder cyclic code
0	0000	0000	00000	0000	0011	0010
1	0001	0001	0001	0001	0100	0110
2	0010	0010	0010	0010	0101	0111
3	0011	0011	0011	0011	0110	0101
4	0100	0100	0100	0100	0111	0100
5	0101	0101	1000	1011	1000	1100
6	0110	0110	1001	1100	1001	1101
7	0111	0111	1010	1101	1010	1111
8	1000	1000	1011	1110	1011	1110
9	1001	1001	1100	1111	1100	1010