C code for Base (Radix) Conversion

In most cases, this is done with printf, but if there are only a few simple needs, including the entire printf function in the program, and it's memory use, can be avoided.

12 bit binary to 3 ASCII HEX digits

//convert lowest 12 bits binary into hex string with trailing zero
//So if value = 0x02F8 string will contain "2F8\0"

unsigned int value = value to convert;
unsigned char byte;
unsigned char string[4];
for (int i = 0; i < 3; i++) {
	var = value & 0x0F;
	value <<= 4;
	if (var <= 9) // 0..9
		string[i] = var + 0x30;
	else // A..F
		string[i] = var + 0x41 - 10;
	}
string[3] = '\0';

12 bit binary to 4 ASCII Decimal Digits

//simple, somewhat slow function to convert binary to ASCII decimal

unsigned int value = value to convert;
const unsigned int digits[4] = {1000, 100, 10,1};
unsigned char string[5];
for (int i = 0; i<4; i++) {
	string[i] = '0';
	while (value >= digits[i]) {value -= digits[i]; string[i]++;}
	}
string[4] = '\0';

Note that the comparison (value>=digits[i]) can only be accomplished by subtracting digits[i] from value, which must then be re-calcuated if the comparison is true. Only a very smart C compiler would optimize that by retaining the result of the comparison. The code can be optimized by doing the subtraction first, then breaking out of the while (recode as for) if the result is negative and incrementing string[i] if it is positive. In that case, digits[i] must be added back into the value, or the original for loop can be expanded into 4 seperate loops were the second and forth ADD the digits array value rather than subtract it then test for a positive value to exit the loop, and increment string while the value is still negative.

16 Bit Binary to 5 ASCII Decimal Digits

from: http://www.cs.uiowa.edu/~jones/bcd/decimal.html Very nice tutorial on decimal conversions

Note that all the multiplications in the code can be replaced by shifts and adds (see: Novel Methods of Integer Multiplication and Division ) in order to avoid the use of a math library when coding for a processor without hardware multiply.

    void putdec( short int n )
    {
        unsigned char d4, d3, d2, d1, d0, q;

        if (n < 0) {
            putchar( '-' );
            n = -n;
        }

        d1 = (n>>4)  & 0xF;
        d2 = (n>>8)  & 0xF;
        d3 = (n>>12) & 0xF;

        d0 = 6*(d3 + d2 + d1) + (n & 0xF);
        q = (d0 * 0xCD) >> 11;
        d0 = d0 - 10*q;

        d1 = q + 9*d3 + 5*d2 + d1;
        q = (d1 * 0xCD) >> 11;
        d1 = d1 - 10*q;

        d2 = q + 2*d2; 
        q = (d2 * 0x1A) >> 8;
        d2 = d2 - 10*q;

        d3 = q + 4*d3;
        d4 = (d3 * 0x1A) >> 8;
        d3 = d3 - 10*d4;

        putchar( d4 + '0' );
        putchar( d3 + '0' );
        putchar( d2 + '0' );
        putchar( d1 + '0' );
        putchar( d0 + '0' );
    }

Divide by 10

On processors without a hardware multiply, base conversion from binary to decimal can be accomplished easily by approximating division by ten.

From: http://www.cs.uiowa.edu/~jones/bcd/divide.html

Code to quickly approximate Q=A/10 to 17 bits (or A < 534,890)

	unsigned int A;
	unsigned int Q; /* the quotient */

	Q = ((A >> 1) + A) >> 1; /* Q = A*0.11 */
	Q = ((Q >> 4) + Q)     ; /* Q = A*0.110011 */
	Q = ((Q >> 8) + Q) >> 3; /* Q = A*0.00011001100110011 */
        /* either Q = A/10 or Q+1 = A/10 for all A < 534,890 */

Code to quickly approximate Q=A/10 to 32 bits

	unsigned long int A;
	unsigned long int Q; /* the quotient */

	Q = ((A >>  1) + A) >> 1; /* Q = A*0.11 */
	Q = ((Q >>  4) + Q)     ; /* Q = A*0.110011 */
	Q = ((Q >>  8) + Q)     ; /* Q = A*0.11001100110011 */
	Q = ((Q >> 16) + Q) >> 3; /* Q = A*0.000110011001100110011001100110011 */
        /* either Q = A/10 or Q+1 = A/10 for all 32-bit unsigned A */

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