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Quater-imaginary base
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===Example: Addition=== Below are two examples of adding in the quater-imaginary system: <pre> 1 β 2i 1031 1 β 2i 1031 ------ + <=> ---- + 2 β 4i 1022 3 β 4i 1023 1 β 8i 1001 ------ + <=> ----- + 4 β12i 12320 </pre> 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 "2''i''s column"), giving 6; 6 is greater than 3, so we subtract 4 (giving 2 as the result in the second column) and carry β1 into the fourth column. Adding the 0s in the third column gives 0; and finally adding the two 1s and the carried β1 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 β1 into the third column (the "β4s column"). Then we add 2+0 in the second column, giving 2. In the third column, we have 0+0+(β1), because of the carry; β1 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 <math>12320_{2i}</math>.
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