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# W4-one - 198:211 Computer Architecture Lecture 6 Fall 2009...

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198:211 Computer Architecture 198:211 Computer Architecture z Topics: z Data representation 2.1 and 2.2 in book z Floating point 2.4 in book Lecture 6 Fall 2009

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Computer Architecture z What do computers do? z Manipulate stored information z Manipulation: operations … more on this later z Information is data: how is it represented? z Basic information: numbers z Human beings have represented numbers throughout history z Roman numerals z Decimal system Discoveregypt.com
Number System z Comprises of z Set of numbers or elements z Operations on them z Rules that define properties of operations z Need to assign value to numbers z Let us take decimal z 1s place, 10s place, 100s place etc z Base 10 z Value= z Humans use decimal × i i 10

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Binary numbers z Base 2; each digit is 0 or 1 z Each bit in place i has value 2 i z Binary representation is used in computers z Easy to represent by switches (on/off) z Manipulation by Digital logic in hardware z But hard for humans to read z (13) 10 = (1101) 2
Hexadecimal representation z Binary hard to read for humans z Especially 16 bits, 32 bits, 64 bits z Base 16 representation or hex representation z Symbols ={0,1,2,3,4,5,6,7,8,9,A,B,C,D,E,F} z Value = z First 10 (0 through 9) symbols are same as decimal z A=10,B=11,C=12, D=13, E=14, F=15 × i i 16

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Decimal to binary z Example: Convert 10 in decimal to binary z Above code works for any base z For hex, replace N%2 by N%16 and replace reminders > 9 by A, B, C, D, E and F z Example: Convert 240 to HEX main(){ int N,i=0; int Maxbits=32; char bitarray[Maxbits] while (N > 0){ bitarray[i]=N%2;i++; N=N/2; }
Binary to decimal z Convert 110110 to decimal z Value = i*2 i z Value = 2 5 2 4 2 2 2 1 z = 32+ 16 + 4 + 2 z = 54 z z

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Converting Hex to binary z Each digit in Hex can be represented by 4 bit binary (base 16) or nibble z Convert 2A8C to binary z 0010 1010 0100 1100
z Group binary bits into groups of four z Replace each nibble by a hex digit z Example 1011011110011100 z 1011 0111 1001 1100 z

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## This note was uploaded on 03/24/2011 for the course CS 211 taught by Professor Chakraborty during the Spring '08 term at Rutgers.

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W4-one - 198:211 Computer Architecture Lecture 6 Fall 2009...

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