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# Class Note for MATH 2303 at UH

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This 8 page Class Notes was uploaded by an elite notetaker on Friday February 6, 2015. The Class Notes belongs to a course at University of Houston taught by a professor in Fall. Since its upload, it has received 18 views.

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Date Created: 02/06/15
Math 2303 Section 43 PlaceValue Systems with Other Bases We already know 0 The positionvalues in the HinduArabic system are 104103102101 0 The positionvalues in the Babylonian system are 604603602601 o The numbers und are called the E3 the HinduArabic and Babylonian systems respectively Now we want to consider other numbers as the base for a system of numeration Some preliminaries 0 Any natural number can serve as a base for a placevalue system of numeration Ten is the natur choice for the base of a system of numeration because most humans have 10 fingers Other bases that are useful include base 2 binary and base 8 in computers For a system with base b you need symbols for the numbers 012 bl So for a base 8 system your numerals would be 0 l 2 3 4 5 6 and 7 For ease we will use the HinduArabic numerals but we could use any symbols we wanted to We will then write numbers with a position Value that is a multiple of the base just like we do base 10 The convention we will use is to write base 10 numbers regularly and to indicate a number is in a different base by a subscript 113 13s For example the number 135348 is a base 8 number You will need to be able to convert from base 10 to another base and Vice versa Example 1 Write 159 as a base 7 number Procedure Use repeated upsidedown division Record the quotient underneath and the remainder out to the right Note that in expanded fonn for base 7 159 3x721gtlt75 Example 2 Wn39te 496 as a base 5 number g M46 5 145 K a 5 a 5L 0 K 3w Example 3 Wm39te 2548 as a base 8 number ls Hk 9 29 2H aL H i 91 011 LHL g Example 4 Wn39te 123 as a base 2 number 1amp2 2L3 K 130 K 11 R0 1 1 Q 2L 8 l E1 HllDHL Converting from another base to base 10 Given a number expressed in a different base to express it as a base 10 number write the expanded version in the base given and then multiply and add Example 5 Write 10110012 as abase 10 number 7 ox12 ox239 1 W 439 W oa o 1 1 39 L 3 03b 1ae3quot lse Example 6 Write 20218 as a base 10 number 1 load 4 0 4 bl Jr oaes 1 l Example 7 Wm39te 432415 as a base 10 number Luca 4 3 531 sl H ll ngo 4 37539 so 10 1 Example 8 Wm39te 101111012 as abase 10 number

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