AVR Freaks

BCD - Binary Coded Decimal

Binay Coded Decimal is a coding trick that eases the storage and conversion of binary numbers, say a count of the crystal beats, to decimal numbers, like you’d want to display on a watch LCD. We can divide an 8-bit byte into two 4-bit nibbles each of which can represent a number with a range of 0 to 16. That’s one of the reasons for the use of hexadecimal notation discussed earlier. And it allows us to store as single decimal integers, 0 to 9, in a nibble and two in a byte, one integer in each nibble. 

If a the decimal number in a byte is less than 99, we can convert it to a BCD byte using the following algorithm:

Set the initial byte (in C we use char) to some two digit value.

	char initialbyte = 54; 
	
Declare a variable for the upper nibble value.
	
   	 char high = 0;
    
Count the tens in initialbyte.

    	while (initialbyte >= 10)               
    	{
        		high++;
        		initialbyte -= 10;
    	}

After this runs the initialbyte now contains only the ones integer from the original byte and high char contains the tens, that is: high = 5 and intialbyte = 4. We combine the high and low nibbles to get the converted byte.

    	convertedbyte  =  (high << 4) | initialbyte;      

This algorithm is used in the CHAR2BCD2 function in the software.

Converting a byte to the ASCII equivalent decimal character using BCD.

We define two bytes Tens and Ones and a third byte, Number, which we set to a value in the range of 0 to 99.
	
	char Tens = 0;
	char Ones = 0;
char Number = 54;

We use the character to BCD algorithm written as the function CHAR2BCD2(char) in the software section below to convert the Number to the BCD equivalent in Tens.

    	Tens = CHAR2BCD2(Number);   
       
Now Tens has the BCD of the tens in the upper nibble and of the ones in the lower nibble. We can convert this to an ASCII character for the integer by remembering that the numerical value of ASCII ‘0’ is 48 and each following char integer is a simple increment of the previous one. Meaning that adding the number 4 to the value of the ASCII character ‘0’, which is  48, yields the ASCII character ‘4’,  (48+4 = 52 which is the ASCII decimal value of the character ‘4’). So the conversion of a decimal integer to its ASCII equivalent character is the simple addition of 48 to the decimal integer.

Since the CHAR2BCD2 function loaded both the tens and ones parts of Number into Tens, we need to extract the Ones and the Tens so that we can add 48 to get the ASCII characters for Number. 

	Ones = Tens;
    	Ones = (Ones & 0x0F) + '0'; 

Finally we get the Tens by right shifing the byte 4-bits, which we use as the ASCII character offset.

    	Tens = (Tens >> 4) + '0';