Sum of strings without converting You have to take 2 string inputs and output the sum of these two strings without converting them to int or using any numeric data type.

ex.

string one = "123";
string two = "456";    
string sum = "579";


Assume the strings won't be larger than 10 digits. 

This is code golf and shortest answer in characters wins. An edit to the answer in C#  will make me smile :). 

Edit: 
Converting to int can be defined as anything of this nature 

Int.TryParse, (int), Convert.ToInt etc
80836 Assembly (57 53 bytes)

53 55 89 E5 8B 4D 0C 8B 55 10 B0 0A 30 DB 88 CF 00 C1 00 C2 49 4A 8A 01 8A 22 00 E0 00 D8 2C 30 30 DB 3C 39 7E 04 B3 01 2C 0A 88 01 88 22 38 CF 75 E2 5D 5B C3


This adds, digit by digit, right to left, without converting ascii digits '0'-'9' to the integers 0-9, and carrying over as needed. The bytecode is the code for a function, which may be called in C (see below). 

The above bytecode was written by hand, from the following assembly (NASM-style, commented):

; save ebx, ebp
push ebx        ; 53
push ebp        ; 55
; copy esp
mov ebp, esp    ; 8B EC
; load arguments
mov ecx, [ebp+0x0C] ; 8B 4D 0C
mov edx, [ebp+0x10] ; 8B 55 10
; initialize stuff
mov al, 10      ; B0 0A
xor bl, bl      ; 30 DB
mov bh, cl      ; 88 CF
; send edx, ecx to end of string
add cl, al     ; 00 C1
add dl, al     ; 00 C2

; decrement everything
dec ecx         ; 49
dec edx         ; 4A

; get rightmost unprocessed digit of each number
mov al, [ecx]   ; 8A 01
mov ah, [edx]   ; 8A 22

; add two ascii digits
add al, ah      ; 00 E0
; add carry if needed
add al, bl      ; 00 D8
; subtract 0x30 ('0') to get the resulting ascii digit
sub al, 0x30    ; 2C 30

; set bl to 0
xor bl, bl      ; 30 DB

; if greater than '9': must carry over to next place
cmp al, 0x39    ; 3C 39
jle $+6         ; 7E 04
; set bl to 1 if carrying over
mov bl, 1       ; B3 01
; subtract 10 from ascii digit if carrying over
sub al, 0x0A    ; 2C 0A

mov [ecx], al   ; 88 01
mov [edx], ah   ; 88 22


; check if loop has ended
cmp bh, cl      ; 38 CF
jne $-28        ; 75 E2

; restore ebx, ebp
pop ebp         ; 5D
pop ebx         ; 5B
; return
ret             ; C3


To try this in C (gcc, linux, intel processor):


#include &lt;stdio.h&gt;
#include &lt;string.h&gt;
#include &lt;sys/mman.h&gt;

int main(){
    // bytecode from earlier
    char code[] = {
        0x53, 0x55, 0x8B, 0xEC, 0x8B, 0x4D, 0x0C, 0x8B, 
        0x55, 0x10, 0x31, 0xC0, 0xB0, 0x09, 0x30, 0xDB, 
        0x01, 0xC1, 0x01, 0xC2, 0x40, 0x50, 0x8A, 0x01,
        0x8A, 0x22, 0x00, 0xE0, 0x00, 0xD8, 0x2C, 0x30,
        0x30, 0xDB, 0x3C, 0x39, 0x7E, 0x04, 0xB3, 0x01,
        0x2C, 0x0A, 0x88, 0x01, 0x88, 0x22, 0x58, 0x48,
        0x49, 0x4A, 0x85, 0xC0, 0x75, 0xDF, 0x5D, 0x5B,
        0xC3,
    };
    // allocate executable memory to a function pointer called 'add'
    void __attribute__( (__cdecl__) ) (*add)(char*,char*) = mmap(0,sizeof code,PROT_WRITE|PROT_EXEC,MAP_ANON|MAP_PRIVATE,-1,0);
    memcpy(add, code, sizeof code);

    // test inputs
    char number1[] = "0878295272", number2[] = "8184206821";

    puts(number1);
    puts(number2);

    // call the bytecode as a c function
    add(number1, number2);

    // output is in the first argument
    puts(number1);

    // release allocated memory
    munmap(add, sizeof code);

    return 0;
}