Convert binary ( integer and fraction) from VHDL to decimal, negative value in C code

Question

I have a 14-bit data that is fed from FPGA in vhdl, The NIos II processor reads the 14-bit data from FPGA and do some processing tasks, where Nios II system is programmed in C code

The 14-bit data can be positive, zero or negative. In Altera compiler, I can only define the data to be 8,16 or 32. So I define this to be 16 bit data.

First, I need to check if the data is negative, if it is negative, I need to pad the first two MSB to be bit '1' so the system detects it as negative value instead of positive value.

Second, I need to compute the real value of this binary representation into a decimal value of BOTH integer and fraction.

I learned from this link (Correct algorithm to convert binary floating point "1101.11" into decimal (13.75)?) that I could convert a binary (consists of both integer and fraction) to decimal values.

To be specified, I am able to use this code quoted from this link (Correct algorithm to convert binary floating point "1101.11" into decimal (13.75)?) , reproduced as below:

#include <stdio.h>
#include <math.h>

double convert(const char binary[]){
  int bi,i;
  int len = 0;
  int dot = -1;
  double result = 0;

  for(bi = 0; binary[bi] != '\0'; bi++){
    if(binary[bi] == '.'){
      dot = bi;
    }
    len++;
  }
  if(dot == -1)
    dot=len;

  for(i = dot; i >= 0 ; i--){
    if (binary[i] == '1'){
      result += (double) pow(2,(dot-i-1));
    }
  }
  for(i=dot; binary[i] != '\0'; i++){
    if (binary[i] == '1'){
      result += 1.0/(double) pow(2.0,(double)(i-dot));
    }
  }
  return result;
}

int main()
{
   char  bin[] = "1101.11";
   char  bin1[] = "1101";
   char  bin2[] = "1101.";
   char  bin3[] = ".11";

   printf("%s -> %f\n",bin, convert(bin)); 
   printf("%s -> %f\n",bin1, convert(bin1)); 
   printf("%s -> %f\n",bin2, convert(bin2)); 
   printf("%s -> %f\n",bin3, convert(bin3)); 

   return 0;
}

I am wondering if this code can be used to check for negative value? I did try with a binary string of 11111101.11 and it gives the output of 253.75...

I have two questions:

1. What are the modifications I need to do in order to read a negative value?

I know that I can do the bit shift (as below) to check if the msb is 1, if it is 1, I know it is negative value...

if (14bit_data & 0x2000) //if true, it is negative value

The issue is, since it involves fraction part (but not only integer), it confused me a bit if the method still works...

2. If the binary number is originally not in string format, is there any way I could convert it to string? The binary number is originally fed from a fpga block written in VHDL say, 14 bits, with msb as the sign bit, the following 6 bits are the magnitude for integer and the last 6 bits are the magnitude for fractional part. I need the decimal value in C code for Altera Nios II processor.

Answer 1

I think this should work:

float convert14BitsToFloat(int16_t in)
{
    /* Sign-extend in, since it is 14 bits */
    if (in & 0x2000) in |= 0xC000;

    /* convert to float with 6 decimal places (64 = 2^6) */
    return (float)in / 64.0f;
}

To convert any number to string, I would use sprintf. Be aware it may significantly increase the size of your application. If you don't need the float and what to keep a small application, you should make your own conversion function.