July 2002
Intermediate to advanced
320 pages
8h 15m
English
Content preview from Hacker's Delight
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12-3. Other Bases
The base − 1 − i has essentially the same properties as the base − 1 + i discussed above. If a certain bit pattern represents the number a + bi in one of these bases, then the same bit pattern represents the number a − bi in the other base.
The bases 1 + i and 1 − i can also represent all the complex integers, using only 0 and 1 for digits. These two bases have the same complex-conjugate relationship to each other, as do the bases −1 ± i. In bases 1 ± i, the representation of some integers has an infinite string of 1’s on the left, similar to the two’s-complement representation of negative integers. This arises naturally by using uniform rules for addition and subtraction, as in the case of two’s-complement. One such integer ...
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