Ch2 - EE306 IntroductiontoComputing...

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Ramesh Yerraballi 2-1 EE 306 Introduction to Computing Chapter 2: Bits, Data Types and  Operations 
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Ramesh Yerraballi 2-2 Data Representation Symbols Numbers: 0,1,2 . .9 Alphabet: A-Z,a-z Other: +*-=/… Why not use multiple  voltages to represent  Numbers? Say 0v = 0; 0.1v=1;  0.2v=2;… Keep it simple Binary  Presence of voltage  -> 1 Absence of voltage  -> 0 Notation lengthy but  easy!
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Ramesh Yerraballi 2-3 Decimal Numbers “decimal” means that we have ten  digits to use in our  representation (the symbols  0 through 9) What is 3,546? it is  three  thousands  plus  five  hundreds  plus  four  tens  plus  six   ones . How about negative numbers? we use two more symbols  to distinguish positive and negative:  +  and  -
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Ramesh Yerraballi 2-4 Unsigned Binary Integers 3-bits 5-bits 8-bits 0 000 00000 00000000 1 001 00001 00000001 2 010 00010 00000010 3 011 00011 00000011 4 100 00100 00000100 Y = “abc” = a.2 2 + b.2 1 + c.2 0 N = number of bits Range is: 0 i < 2 N - 1 (where the digits a, b, c can each take on the values of 0 or 1 only) Problem: How do we represent negative numbers?
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Ramesh Yerraballi Signed Magnitude Leading bit is the sign  bit -4 10100 -3 10011 -2 10010 -1 10001 -0 10000 +0 00000 +1 00001 +2 00010 +3 00011 +4 00100 Range is: -2 N-1 + 1 < i < 2 N-1 - 1 Y = “abc” = (-1) a (b.2 1 + c.2 0 ) Problems: How do we do addition/subtraction? We have two numbers for zero (+/-)!
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Ramesh Yerraballi 2-6 One’s Complement Invert all bits -4 11011 -3 11100 -2 11101 -1 11110 -0 11111 +0 00000 +1 00001 +2 00010 +3 00011 +4 00100 Range is: -2 N-1 + 1 < i < 2 N-1 - 1 If msb (most significant bit) is 1 then the number is negative (same as signed magnitude) Problems: Same as for signed magnitude
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Ramesh Yerraballi 2-7 Two’s Complement - Idea Arithmetic Logic Unit  (ALU) part of the CPU  performs all  computations Nice to have a  representation for binary  numbers so that, A+ (-A)  = 0 (when we add a 
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Ch2 - EE306 IntroductiontoComputing...

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