# lec3 - CSE20 Lecture 3 Number Systems Negative Numbers 1...

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Unformatted text preview: CSE20 Lecture 3 Number Systems: Negative Numbers 1. Sign and Magnitude Representation 2. 1’s Complement Representation 3. 2’s Complement Representation 1 CK Cheng, UC San Diego 2 Outlines 1.Goal of the Negative Number Systems 2.Definition 1.Sign Magnitude Rep. 2.1’s Complement Rep. 3.2.s Complement Rep. 3.Arithmetic Operations Goal of negative number systems • Signed system: Simple. Just flip the sign bit • 0 = positive • 1 = negative • One’s complement: Replace subtraction with addition – Easy to derive (Just flip every bit) • Two’s complement: Replace subtraction with addition – Addition of one’s complement and one produces the two’s complement. 3 Definitions: Given a positive integer x, we represent -x • 1’s complement: Formula: 2 n -1 – x • i.e. n=4, 2 4 – 1 – x = 15 – x • In binary: (1 1 1 1) – (b 3 b 2 b 1 b ) • Just flip all the bits. • 2’s complement: Formula: 2 n –x • i.e. n=4, 2 4 – x = 16 – x • In binary: ( 1 0 0 0 0) – ( b 3 b 2 b 1 b ) • Just flip all the bits and add 1. 4 5 Definitions: 4-Bit Example Definitions: Examples Given n-bits, what is the range of my numbers in each system?...
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lec3 - CSE20 Lecture 3 Number Systems Negative Numbers 1...

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