cse20 lecture 2 - CSE20 Lecture 2: Number Systems: Binary...

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CSE20 Lecture 2: Number Systems: Binary Numbers, Gray Code, and Negative Numbers CK Cheng WI’10 7 January 2010 1
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Number Systems 1. Introduction 2. Binary Numbers 3. Gray code 4. Negative Numbers 5. Residual Numbers 2
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2. Binary Numbers b 2 b 1 b 0 Value 0 0 0 0 0 0 1 1 0 1 0 2 0 1 1 3 1 0 0 4 1 0 1 5 1 1 0 6 1 1 1 7 8 4 2 1 0 0 1 1 0 1 0 1 1 0 0 0 3 + 5 = 8 8 4 2 1 0 0 1 1 0 1 1 0 1 0 0 1 3 + 6 = 9 + + Examples : (3) (5) (8) (3) (6) (9) This is a non-redundant number system 3
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2. Binary Cont. a b Carry Sum 0 0 0 0 0 1 0 1 1 0 0 1 1 1 1 0 id a b c Carry Sum 0 0 0 0 0 0 1 0 0 1 0 1 2 0 1 0 0 1 3 0 1 1 1 0 4 1 0 0 0 1 5 1 0 1 1 0 6 1 1 0 1 0 7 1 1 1 1 1 2*0 + 0 = 0 0 0 id 0 2*0 + 1 = 0 0 1 id 1 2*1 + 0 = 1 1 0 id 6 2*1 + 1 = 1 1 1 id 7 RULE: 2 x Carry + Sum = a + b + c 4
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3. Gray Code reflection Low power (reliability) when the numbers are consecutive in series. The idea is to only change ONE bit at a time. e.g. addresses, analog signals NOTE: Not for arithmetic operations (the rule is too complicated) 5
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4. Negative Numbers Given a positive integer x, represent the negative integer –x in (b n-1 , …, b 0 ) (i) Signed bit system
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This note was uploaded on 06/12/2011 for the course CS 1 taught by Professor Staff during the Fall '08 term at Cornell University (Engineering School).

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cse20 lecture 2 - CSE20 Lecture 2: Number Systems: Binary...

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