Quater-imaginary Base - Addition and Subtraction - Example: Addition

Example: Addition

Below are two examples of adding in the quater-imaginary system:

1 - 2i 1031 3 - 4i 1023 1 - 2i 1031 1 - 8i 1001 ------- + <=> ----- + ------- + <=> ----- + 2 - 4i 1022 4 - 12i 12320

In the first example we start by adding the two 1s in the first column (the "ones' column"), giving 2. Then we add the two 3s in the second column (the "2is column"), giving 6; 6 is greater than 3, so we subtract 4 (giving 2 as the result in the second column) and carry −1 into the fourth column. Adding the 0s in the third column gives 0; and finally adding the two 1s and the carried −1 in the fourth column gives 1.

In the second example we first add 3+1, giving 4; 4 is greater than 3, so we subtract 4 (giving 0) and carry −1 into the third column (the "−4s column"). Then we add 2+0 in the second column, giving 2. In the third column, we have 0+0+(−1), because of the carry; −1 is less than 0, so we add 4 (giving 3 as the result in the third column) and "borrow" +1 into the fifth column. In the fourth column, 1+1 is 2; and the carry in the fifth column gives 1, for a result of .