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:::''b'' is one less than the number of digits. S has 17 binary digits because it lies between 2^16 and 2^17 so ''b'' = 16 and your method gives an estimate of 2^8 = 256, the same as the method in the article. The actual square root of S is about 354. [[User:Gandalf61|Gandalf61]] ([[User talk:Gandalf61|talk]]) 16:19, 13 July 2013 (UTC)
::::OK, so then we actually have the even case which is equivalent to the formula above. Sorry for the confusion. [[User:Isheden|Isheden]] ([[User talk:Isheden|talk]]) 16:45, 13 July 2013 (UTC)
What I was actually mainly thinking of is the relevance of treating even and odd number of digits separately in the decimal case. For the example given, starting with 300 instead of 600 actually yields the answer to six significant figures in one iteration less. While this is surely just a coincidence, the question is if the extra effort is warranted? [[User:Isheden|Isheden]] ([[User talk:Isheden|talk]]) 17:03, 13 July 2013 (UTC)
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