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Need to convert data (byte value into hex and hex characters as ASCII characters)

Working: I am reading a byte from memory (EEPROM/FLASH etc) and then i want to send this byte to computer not as actual value but as a ascii characters of its hex value. eg i read 160 from memory, which is 0xA0 in hex, now i want to send this number not as 160 but as 'A' and '0' (which are 0x41 and 0x30), for this i am using this type of c code in MPLAB IDE,

    //Here is the code for Parity:
    uint8_t unAddParitytoByte(uint8_t unByte)
    { 
           uint8_t unNumberofOnes = 0;
           for(uint8_t unI = 0x80; unI ; unI>>=1)
           {
                 if((unByte & unI) != 0)
                {
                     unNumberofOnes++;
                }
          }
          if((unNumberofOnes%2) == 0)
          {
                  return unByte;
          }
          else
          {
               return (unByte|BIT7);
          }
    }
    void vSendByteToSoftware(uint8_t unDataByte)
    {
        uint8_t unTemp = 0, unHalfByte = 0;
        unTemp = (unDataByte >> 4) & 0x0F;
        unHalfByte = unReturnASCII(unTemp);
    /*Ignore vSerialTransmitCharacter(); as it transmit through uart and unAddParitytoByte(); to add 8th bit parity*/
        vSerialTransmitCharacter(unAddParitytoByte(unHalfByte)); 
        unBCCByte ^= unAddParitytoByte(unHalfByte);
        unTemp = unDataByte & 0x0F;
        unHalfByte = unReturnASCII(unTemp);
        vSerialTransmitCharacter(unAddParitytoByte(unHalfByte));
        unBCCByte ^= unAddParitytoByte(unHalfByte);
    }
    uint8_t unReturnASCII(uint8_t unNibble)
    {
         uint8_t unChar = 0;
         switch(unNibble)
         {
            case 0:
                 unChar = '0';
                 break;
            case 1:
                 unChar = '1';
                 break;
            case 2:
                 unChar = '2';
                 break;
            case 3:
                 unChar = '3';
                 break;
            case 4:
                 unChar = '4';
                 break;
            case 5:
                 unChar = '5';
                 break;
            case 6:
                 unChar = '6';
                 break;
            case 7:
                 unChar = '7';
                 break;
            case 8:
                 unChar = '8';
                 break;
            case 9:
                 unChar = '9';
                 break;
            case 10:
                 unChar = 'A';
                 break;
            case 11:
                 unChar = 'B';
                 break;
            case 12:
                unChar = 'C';
                break;
            case 13:
                unChar = 'D';
                break;
            case 14:
                unChar = 'E';
                break;
            case 15:
                unChar = 'F';
                break;
            default:
                break;
        }
        return unAddParitytoByte(unChar);
    }
    vSendByteToSoftware(unReadBytesfromTargetFlash());

I hope this is understandable. Problem: My concern is that i have a controller with frequency 3.6864MHz and i have to perform this operation on almost 1M bytes or more, so its a lot time consuming.

I was wondering if there is advance and fastest approach to this process for every single byte which can make my operation pretty fast?

Note:(Baud rate is 115200 which is quite fast and i want speed in processing bytes rather than time to send them.)

Each half-byte has sixteen possible values which are sequential and start with zero. This is ideal for a lookup table.

    uint8_t const ascii_hex[16] = { '0', '1', '2', '3', '4', '5', '6', '7', '8', '9', 'A', 'B', 'C', 'D', 'E', 'F'};

    void vSendByteToSoftware(uint8_t unDataByte)
    {
        uint8_t unTemp = 0, unHalfByte = 0;
        unTemp = (unDataByte >> 4) & 0x0F;
        unHalfByte = ascii_hex[unTemp];
    /*Ignore vSerialTransmitCharacter(); as it transmit through uart and unAddParitytoByte(); to add 8th bit parity*/
        vSerialTransmitCharacter(unAddParitytoByte(unHalfByte)); 
        unBCCByte ^= unAddParitytoByte(unHalfByte);
        unTemp = unDataByte & 0x0F;
        unHalfByte = ascii_hex[unTemp];
        vSerialTransmitCharacter(unAddParitytoByte(unHalfByte));
        unBCCByte ^= unAddParitytoByte(unHalfByte);
    }

Update : Since the characters you are transmitting are limited to the set of sixteen, you can precalculate the parity for these sixteen characters and then use a lookup table to get the parity value. (Please double check whether I've done the parity calculations correctly.)

uint8_t const ascii_hex[16] = { '0', '1', '2', '3', '4', '5', '6', '7', '8', '9', 'A', 'B', 'C', 'D', 'E', 'F'};
uint8_t const ascii_hex_with_parity[16] = { 0x30, 0xB1, 0xB2, 0x33, 0xB4, 0x35, 0x36, 0xB7, 0xB8, 0x39, 0x41, 0x42, 0xC3, 0x44, 0xC5, 0xC6};

void vSendByteToSoftware(uint8_t unDataByte)
{
    uint8_t unTemp = 0, unHalfByte = 0;
    unTemp = (unDataByte >> 4) & 0x0F;
    unHalfByte = ascii_hex[unTemp];
/*Ignore vSerialTransmitCharacter(); as it transmit through uart and unAddParitytoByte(); to add 8th bit parity*/
    vSerialTransmitCharacter(unAddParitytoByte(unHalfByte)); 
    unBCCByte ^= ascii_hex_with_parity[unTemp];
    unTemp = unDataByte & 0x0F;
    unHalfByte = ascii_hex[unTemp];
    vSerialTransmitCharacter(unAddParitytoByte(unHalfByte));
    unBCCByte ^= ascii_hex_with_parity[unTemp];
}

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