Quater-imaginary Base - Multiplication

Multiplication

For long multiplication in the quater-imaginary system, the two rules stated above are used as well. When multiplying numbers, multiply the first string by each digit in the second string consecutively and add the resulting strings. With every multiplication, a digit in the second string is multiplied with the first string. The multiplication starts with the rightmost digit in the second string and then moves leftward by one digit, multiplying each digit with the first string. Then the resulting partial products are added where each is shifted to the left by one digit. An example:

11201 20121 x -------- 11201 <--- 1 x 11201 12002 <--- 2 x 11201 11201 <--- 1 x 11201 00000 <--- 0 x 11201 12002 + <--- 2 x 11201 ------------ 120231321

This corresponds to a multiplication of .