Here we need 3 columns, one each for the multiplicands and one for the result.
Our example will be 12 * 61 = XII * LXI. I chose this example so that we don't need to use negative digits; negative digits can be handled easily, but you can get the idea without them.
We start with the operands on the first two columns. 12 has one pebble at the X row and 2 at the units row; 61 has one pebble at the L row, one at the X row and one at the I row. The column for the result is now empty.
D | ||
C | ||
———————————————
L | o ||
X o | o ||
———————————————
V | ||
I oo| o ||
———————————————
We start removing pebbles from the first multiplicand. For each pebble in the multiplicand, we perform the multiplication with the second multiplicand, which in our case means we "copy" the multiplicand in the results column with an appropriate shift in rows. Since the first mutiplicand has 3 pebbles, there are three steps:
Step 1:
D | ||
C | ||
———————————————-
L | o || o
X o | o || o
———————————————-
V | ||
I o | o || o
———————————————-
Step 2:
D | ||
C | ||
———————————————-
L | o || oo
X o | o || oo
———————————————-
V | ||
I | o || oo
———————————————-
Step 3:
D | || o
C | || o
———————————————-
L | o || oo
X | o || oo o
———————————————-
V | ||
I | o || oo
———————————————-
So, the result is DCLLXXXII. Of course, LL is not really "legal", so we replace it with a C, so we get DCCXXXII, or 732, which is indeed the correct number.
Multiplication of Roman numerals.
Here we need 3 columns, one each for the multiplicands and one for the result.
Our example will be 12 * 61 = XII * LXI. I chose this example so that we don't need to use negative digits; negative digits can be handled easily, but you can get the idea without them.
We start with the operands on the first two columns. 12 has one pebble at the X row and 2 at the units row; 61 has one pebble at the L row, one at the X row and one at the I row. The column for the result is now empty.
We start removing pebbles from the first multiplicand. For each pebble in the multiplicand, we perform the multiplication with the second multiplicand, which in our case means we "copy" the multiplicand in the results column with an appropriate shift in rows. Since the first mutiplicand has 3 pebbles, there are three steps:Step 1:
Step 2: Step 3: So, the result is DCLLXXXII. Of course, LL is not really "legal", so we replace it with a C, so we get DCCXXXII, or 732, which is indeed the correct number.