Unsigned Integer to BCD conversion?

Question

I know you can use this table to convert decimal to BCD:

0 0000

1 0001

2 0010

3 0011

4 0100

5 0101

6 01

Answer 1

You know the Binary numeral system, don't you?

Especially have a look at this chapter.

EDIT: Also note KFro's comment that the lower nibble (= 4 bits) of the binary ASCII representation of numerals is in BCD. This makes conversions BCD <-> ASCII very easy as you just have to add/remove the leading 4 bits:

Number    ASCII Code
0         0011 0000
1         0011 0001
 ...
8         0011 1000
9         0011 1001

Answer 2

I know this has been previously answered but I've extended this for unsigned ints of different sizes using a template to build the specific code.

#include <stdio.h>
#include <unistd.h>

#include <stdint.h>

#define __STDC_FORMAT_MACROS
#include <inttypes.h>

constexpr int nBCDPartLength = 4;
constexpr int nMaxSleep = 10000; // Wait enough time (in ms) to check out the boundry cases before continuing.

// Convert from an integer to a BCD value.
// some ideas for this code are from :
//  http://stackoverflow.com/questions/1408361/unsigned-integer-to-bcd-conversion
//  &&
//  http://stackoverflow.com/questions/13587502/conversion-from-integer-to-bcd
// Compute the last part of the information and place it into the result location.
// Decrease the original value to place the next lowest digit into proper position for extraction.
template<typename R, typename T> R IntToBCD(T nValue) 
{
    int nSizeRtn = sizeof(R);
    char acResult[nSizeRtn] {};
    R nResult { 0 };
    int nPos { 0 };

    while (nValue)
    {
        if (nPos >= nSizeRtn)
        {
            return 0;
        }

        acResult[nPos] |= nValue % 10;
        nValue /= 10;

        acResult[nPos] |= (nValue % 10) << nBCDPartLength;
        nValue /= 10;

        ++nPos;
    }

    nResult = *(reinterpret_cast<R *>(acResult));

    return nResult;
}

int main(int argc, char **argv)
{
    //uint16_t nValue { 10 };
    //printf("The BCD for %d is %x\n", nValue, IntToBCD<uint32_t, uint16_t>(nValue));

    // UINT8_MAX    =   (255)                               - 2 bytes can be held in uint16_t (2 bytes)
    // UINT16_MAX   =   (65535)                             - 3 bytes can be held in uint32_t (4 bytes)
    // UINT32_MAX   =   (4294967295U)                       - 5 bytes can be held in uint64_t (8 bytes)
    // UINT64_MAX   =   (__UINT64_C(18446744073709551615))  - 10 bytes can be held in uint128_t (16 bytes)


    // Test edge case for uint8
    uint8_t n8Value { UINT8_MAX - 1 };
    printf("The BCD for %u is %x\n", n8Value, IntToBCD<uint16_t, uint8_t>(n8Value));
    // Test edge case for uint16
    uint16_t n16Value { UINT16_MAX - 1 };
    printf("The BCD for %u is %x\n", n16Value, IntToBCD<uint32_t, uint16_t>(n16Value));
    // Test edge case for uint32
    uint32_t n32Value { UINT32_MAX - 1 };
    printf("The BCD for %u is %" PRIx64 "\n", n32Value, IntToBCD<uint64_t, uint32_t>(n32Value));
    // Test edge case for uint64
    uint64_t n64Value { UINT64_MAX - 1 };
    __uint128_t nLargeValue = IntToBCD<__uint128_t, uint64_t>(n64Value);
    uint64_t nTopHalf = uint64_t(nLargeValue >> 64);
    uint64_t nBottomHalf = uint64_t(nLargeValue);
    printf("The BCD for %" PRIu64 " is %" PRIx64 ":%" PRIx64 "\n", n64Value, nTopHalf, nBottomHalf);

    usleep(nMaxSleep);

    // Test all the values
    for (uint8_t nIdx = 0; nIdx < UINT8_MAX; ++nIdx)
    {
        printf("The BCD for %u is %x\n", nIdx, IntToBCD<uint16_t, uint8_t>(nIdx));
    }

    for (uint16_t nIdx = 0; nIdx < UINT16_MAX; ++nIdx)
    {
        printf("The BCD for %u is %x\n", nIdx, IntToBCD<uint32_t, uint16_t>(nIdx));
    }

    for (uint32_t nIdx = 0; nIdx < UINT32_MAX; ++nIdx)
    {
        printf("The BCD for %u is %" PRIx64 "\n", nIdx, IntToBCD<uint64_t, uint32_t>(nIdx));
    }

    for (uint64_t nIdx = 0; nIdx < UINT64_MAX; ++nIdx)
    {
        __uint128_t nLargeValue = IntToBCD<__uint128_t, uint64_t>(nIdx);
        uint64_t nTopHalf = uint64_t(nLargeValue >> 64);
        uint64_t nBottomHalf = uint64_t(nLargeValue);
        printf("The BCD for %" PRIu64 " is %" PRIx64 ":%" PRIx64 "\n", nIdx, nTopHalf, nBottomHalf);
    }
    return 0;
}

Answer 3

Here is a macro for uint16_t, so that it gets evaluated at compile-time (provided that u is a pre-defined constant). This agrees with dec2bcd() from above up to 9999.

#define U16TOBCD(u) ((((u/1000)%10)<<12)|(((u/100)%10)<<8)|\
                    (((u/10)%10)<<4)|(u%10))

Answer 4

This is from the micro controller world.... Note that values are rounded in the division. For instance 91 to BCD would be 91/10 * 16 = 144 + 91%10 = 145. Converted to Binary is 10010001.

uint8_t bcdToDec(uint8_t val)
{
  return ( (val/16*10) + (val%16) );
}

uint8_t decToBcd(uint8_t val)
{
  return ( (val/10*16) + (val%10) );
}