12 34 56
      78
-- -- --
12 35 34

10
         11-
-- -- -- --
99 99 99 99 (and you still have a borrow).

11
10-
--
 1 (then negate to get -1).

-a +  b becomes b - a
 a + -b becomes a - b

a - -b becomes   a + b
-a -  b becomes -(a + b)

small - big becomes -(big - small)

475(a) x 32(b) = 475 x (30 + 2)
               = 475 x 30 + 475 x 2
               = 4750 x 3 + 475 x 2
               = 4750 + 4750 + 4750 + 475 + 475

457
   +-------
27 | 12345    27 is larger than 1 or 12 so we first use 123.
     108      27 goes into 123 4 times, 4 x 27 = 108, 123 - 108 = 15.
     ---
      154     Bring down 4.
      135     27 goes into 154 5 times, 5 x 27 = 135, 154 - 135 = 19.
      ---
       195    Bring down 5.
       189    27 goes into 195 7 times, 7 x 27 = 189, 195 - 189 = 6.
       ---
         6    Nothing more to bring down, so stop.

457 x 27 + 6
= 12339    + 6
= 12345

123
    x  34
    -----
      492
+    3690
---------
     4182

unsigned char first[1024], second[1024], result[1025];
unsigned char carry = 0;
unsigned int  sum   = 0;

for(size_t i = 0; i < 1024; i++)
{
    sum = first[i] + second[i] + carry;
    carry = sum - 255;
}

9
   +
9
----
18