Generate degree-bound LFSR to approximate given sequence
The measure you are interested in is usually called $k-$error linear complexity. See this review in Asiacrypt 2003 by Niederreiter. There are unpaywalled versions of this paper around. The ...
For what $N$ does $2^N$ overflow?
You don't explain how $2^N$ is calculated, so I'm assuming you repeatedly multiply by 2 (or equivalently, you repeatedly add the number to itself, or shift it left). Here's how this process looks on a ...
Register Transfer Activity
One way this can be performed in a single cycle is through register renaming. If the processor supports register renaming, no data needs to be moved: one simply renames which register is called R1 ...
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