COP3502_13_BaseConversion

COP3502_13_BaseConversion - Base Conversions Computer...

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Computer Science Department University of Central Florida Base Conversions COP 3502 – Computer Science I

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Base Conversion page 2 © Jonathan Cazalas Counting Systems – Basic Info Regular Counting System Known as Decimal also known as base 10 Do you know why it is called base 10? If you said, “because it has ten counting digits”: 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9 You are right! To count in base ten, you go from 0 to 9 Then you count in combinations of two digits starting with 10 all the way to 99 After 99 comes three-digit combinations from 100 – 999, etc.
Base Conversion page 3 © Jonathan Cazalas Counting Systems – Basic Info Regular Counting System Let’s examine a decimal number: When we break down this number, we have: 2 “thousands” + 7 “hundreds” + 1 “tens” + 3 “ones 2000 + 700 + 10 + 3 Let’s see, in detail, how we get this 2 7 1 3 Thousands place Hundreds place Tens place Ones place

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Base Conversion page 4 © Jonathan Cazalas Counting Systems – Basic Info Regular Counting System The decimal number 2713: When we break down this number, we have: 2000 + 700 + 10 + 3 Where does the 2000 come from? How do we get 2000? Mathematically, We said this means we have two “thousands” A thousand is 1000 How do we represent 1000, in terms of 10? So 2000 is the same as 2 x 10 3 10 3 = 2 x 1000 = 2000
Base Conversion page 5 © Jonathan Cazalas Counting Systems – Basic Info Regular Counting System The decimal number 2713: Similarly, The next digit, 7, means that we have 7 “hundreds” We have 7, “100”s Mathematically, how do we represent 100 in terms of 10? 10 2 So 700 comes from 7x10 2 = 7x100 = 700

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Base Conversion page 6 © Jonathan Cazalas Counting Systems – Basic Info Regular Counting System The decimal number 2713: Next: The next digit, 1, means that we have 1 “ten” We have 1, “10” Mathematically, we represent this as 10 1 So 10 comes from 1x10 1 = 1x10 = 10 Finally: The last digit, 3, means that we have 3 “ones” We have 3, “1”s How do we represent 1 in terms of 10? So 3 comes from 3x10 0 = 3x1 = 3 As 10 0 .
Base Conversion page 7 © Jonathan Cazalas Counting Systems – Basic Info Regular Counting System The decimal number 2713: Putting this all together, 2713 10 = 2 x 10 3 + 7 x 10 2 + 1 x 10 1 + 3 x 10 0 What we learn from this: Each digit’s value is determined by the place it is in Each place is a perfect power of the base With the least significant at the end Counting up, by 1, as you go through the number from right to left

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Base Conversion page 8 © Jonathan Cazalas Counting Systems – Basic Info Other Counting Systems At first glance, it may seem that this would be the only possible number system That is, using 10 digits (0 – 9) Turns out, the number of digits used is arbitrary
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COP3502_13_BaseConversion - Base Conversions Computer...

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