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218L2S09

# 218L2S09 - ESE218 Lecture 2 Outline Number systems Binary...

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1/29/2009 ESE218 Spring 2009 Lecture 2 1 ESE218 Lecture 2 Number systems. Binary arithmetic. Negative numbers Outline Number systems: Decimal vs Binary, Octal, Hexadecimal Decimal-to-Binary conversion Binary arithmetic Addition, subtraction, multiplication, division Negative numbers Signed magnitude Complement system Decimal integers with sign 10’s complements 9’s complements Binary integers with sign 1’s complements 2’s complements Summary

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1/29/2009 ESE218 Spring 2009 Lecture 2 2 Positional numbers systems. Decimal and binary digits. Binary Decimal 9 8 7 6 5 4 3 2 1 0 1 0 10 digits 2 digits 1 Bit = Bi nary digit <= Bit position defines the weight of bit 218 10 = 2 x 10 2 + 1 x10 1 + 8 x10 0 11011010 2 = 1x2 7 + 1x2 6 + 1x2 4 + 1x2 3 + 1x2 1 High voltage Low voltage Logical 1 Ù Logical 0 Ù Most digital systems utilize POSITIVE LOGIC: 7 6 5 4 3 2 1 0