4_NumberTheory

4_NumberTheory - Number Systems 9/6/11 Decimal number...

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Number Systems 9/6/11 Decimal number system Binary number system Special bit sequences A position's weight is r k , where k is the number of positions from the decimal point. To the left of the decimal point, k takes values 0, 1, 2. .. , and to the right, it takes values -1,-2,. ..
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Octal number system Hexadecimal number system Examples
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Base-r representation of a decimal integer 1. Let the given integer be denoted N. 2. By the Division Algorithm, there exist unique N 1 and a 0 such that N = N 1 r + a 0 , 0 a 0 < r. a 0 is the first digit (rightmost digit) of base-r representation. 3. Applying the Division Algorithm on N 1 , we get N 1 = N 2 r + a 1 , 0 a 1 < r. a 1 is the next digit (on the left) in base-r representation. 4. Repeat this until quotient is zero. If the Division Algorithm is applied k times, then a k-1 … a 1 a 0 is the base-r representation of N.
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Converting a decimal fraction to base-r notation Let i=-1, the fractional part be denoted as 0.f The digits in the fractional part of base-r notation are denoted 0.a -1 a -2 a -3 1. Multiply 0.f with r
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This note was uploaded on 03/21/2012 for the course CS 3333 taught by Professor Boppana during the Fall '11 term at Texas San Antonio.

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4_NumberTheory - Number Systems 9/6/11 Decimal number...

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