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# L08_blanks - Day 08 Base-B Systems Pencil Paper Algorithims...

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1 Day 08 Base-B Systems Pencil & Paper Algorithims (& their alternatives) 2 Today’s Travel Plans Generalities of Place Value Systems Other Bases The same number? Comparing Classic Pencil & Paper Algorithms Alternative Pencil & Paper Algorithms

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2 3 Last time we learned… Any number of the from can be re-written in the form which is known as a Base-10 , or _____________, expansion . We saw an expansion in Base-10… You may not know this but I was rushing and messed up the Base-5 expansion 4 Some Generalities I’d like to emphasize… In a general place-value system , there are always a unique set of symbols called digits, D = {d 0 , d 1 , …., d n } each with its own face value and a unique set of place values P = {p 0 =1, p 1 , p 3 , …} In a place-value system every number of the form can be rewritten as In a Base-B system every place holder is a power of a common valued called the base , B . Usually the k-thplace value is the k-thpower of the base, that is
3 5 Some Generalities I’d like to emphasize… Therefore, in a general Base-B Place Value System the number written as can be rewritten as This process is called a Base-B Expansion . Two important details about a Base-B system is that they must always have _______ unique digit symbols and The highest face value of any digit must be one ________ than the value of the base. In our system, we have _____ digits, ________________________. The highest face value _____ is one less than the base value _____. 6 Other Bases Our system uses Base-10, thus we have ten digits which were created by Arabic Scholars and Traders.

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L08_blanks - Day 08 Base-B Systems Pencil Paper Algorithims...

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