Parsing a hex nr byte by byte

Question

I'm trying to parse a hex number byte by byte, and concatenate to a string the representation of each byte, in the order they're stored in memory. (for a little test on endianness, but that's not important I guess).

Here is the code (please ignore the glaring unit-test issues with it :D; also, some of the code might look weird since initially the display_bytes method took in a char* not an int8_t*, but I thought using an int8_t might make it more obvious to me, what the issue is)

TEST_CLASS(My001littlebigendian)
{
public:
    
    TEST_METHOD(TestMethod1)
    {
        int i = 0x12345678;

        display_bytes((int8_t*)&i, sizeof(i));
    }

    void display_bytes(int8_t* b, int length)
    {
        std::stringstream ss;
        for (int i = 0; i < length; ++i)
        {
            int8_t signedCharRepresentation = *(b + i); //signed char has 1 byte
            int8_t signed8ByteInt = (int8_t)signedCharRepresentation;       //this is not ok
            int32_t signed32ByteInt = (int32_t)signedCharRepresentation;    //this is ok. why?

            //ss << std::hex << signed8ByteInt; //this is not ok. why?
            ss << std::hex << signed32ByteInt;  //this is ok
        }

        std::string stringRepresentation = ss.str();
        if (stringRepresentation.compare("78563412") == 0)
        {
            Assert::IsTrue(true, L"machine is little-endian");
        }
        else if(stringRepresentation.compare("01234567") == 0)
        {
            Assert::IsTrue(true, L"machine is big-endian");
        }
        else
        {
            Assert::IsTrue(true, L"machine is other-endian");
        }
    }
};

Now, what I don't understand (as hopefull the comments make clear) is why does this only work when I cast each byte to a 4 byte int, and not an 1 byte int. Since I am working with chunks of 1 byte. Intuitively it would make me think doing it like this should cause some sort of overflow? But it seems not.

I've not dug deeper into why this is the issue yet, since I was hoping to not need to. And maybe if someone with more knowledge in this area can give me nudge in the right direction, or maybe even an outright answer if I'm missing something very obvious. (which I do feel I might be, since I'm not used to working at this low level).