Assembly 8086 | Sum of an array, printing multi-digit numbers

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With the correction for the add to be replaced by mov as noted in your comment (Note that the line: add al, [bx] is actually mov al, [bx]) there’s just the function call at the label EndLoop that’s wrong!

You want to display the sum, and are using the DOS print function. This function 09h expects a pointer in DS:DX that you are not providing!
Even if you did, you would still have to convert the sum number in its text representation.

A quick solution here would be to content yourself and just display the result in the form of a single ASCII character. The hardcoded sum is 52 and so it is a displayable character:

EndLoop:
    mov dl, [sum]
    mov ah, 02h    ;Single character output
    int 21h

; --------------------------

exit:
    mov ax, 4c00h
    int 21h

One step further and we can display “52”:

mov al,[sum]
mov ah,0
mov dl,10
div dl        ---> AL=5   AH=2
add ax,3030h  ---> AL="5" AH="2"
mov dh,ah     ;preserve AH
mov dl,al
mov ah,02h
int 21h
mov dl,dh     ;restore
int 21h

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