char to unsigned int

What is your definition of WORD?

As I've said many times before, WORD (and, hence, things like DWORD, etc) is a poor type name because it tells you neither its size nor its signed-ness.
It would be far better to choose a name that explicitly shows both.

I use:
U32 - Unsigned 32 bits
S32 - Signed 32 bits
U16 - Unsigned 16 bits
S16 - Signed 16 bits
etc.

I second Andrew's suggestion. I'd add that you should never trust the implicit signed-ness of the bare "char" declaration, since it varies from compiler to compiler. "U8" is also useful as it clearly makes the distinction between a variable intended as a small integer and a variable intended as human-readable text (a "character").

Do you mean that both forms of the statement posted produce the same result? Or that one produces the expected result and one does not? (If so, which one works?)

The snippet as shown does not initialize chksum_read, so the += leaves you at the mercy of whatever garbage was in the variable. If that happened to be 0xFF00, you would see the described results.

Assuming we're talking about the 8051, if you are going to do a lot of shift by 8s, you might consider a union type.

typedef struct
    {
    U8 byte[2];
    U16 u16;
    } BytewiseU16;

U8 prev_ch;
Bytewise16 chksum_read;

// shift left by 8
chksum_read.byte[0] = chksum_read.byte[1];
chksum_read.byte[1] = 0;

// add prev_ch shifted left by 8
chksum_read[0] += prev_ch;

What is the value of chksum_read before either of the 2 chksum_read += statements?

Is it initialized to 0?

Jon

prev_ch is a unsigned char not char.
word is unsigned int
prev_ch is 0 before calculation.

this is a strange one?