csc255-702/703 cti/depaul1 csc-255 lecture 3 text and numerical storage (chapter 1 from brookshear)...

CSC255-702/703 CTI/DePaul 1

CSC-255

Lecture 3

Text and Numerical Storage(Chapter 1 from Brookshear)

Modified by Ufuk Verun from

Jim Janossy © 2002, DePaul University CTI – Chicagoand

Brookshear © 2003 Pearson Education, Inc.


Resources

This PowerPoint presentation is available for download at www.depaul.edu/~uverun/CSC255/fall2002/slides/Lecture_03.pptTextbook: Chapter 1Print slides at 6 slides/page, avoid waste!Exams are based on slide content, homework and assigned readings


Text

Printable characters A, a, B, b, etc.Each different character is assigned a unique 8-bit pattern See the ASCII chart on page 499, Appendix

AASCII: American Standard Code for Information Interchange

More recent codings use more bits to store more symbols and characters Unicode for Java, 16 bits per character


ASCII

Developed in 1968 originally as a 7-bit code 7 bits can define 128 patterns,

27=128 Extended to 8 bits, 28=256 patterns

Most common code in useEBCDIC is analogous IBM mainframe code, 8-bit, different assignment of codes to characters


ASCII Example

Text “Hello.” coded in ASCII:


Unicode

Developed in 1990’s as a 16-bit code Defines 65,536 patterns, 216

Implemented in JavaReplaces earlier schemes to support non-English characters (such as Chinese and Japanese alphabets)First 128 characters are same as ASCII


Exercise: ASCII Practice

What is “ABCabc” in ASCII?Char Hex BitsA 41 0100 0001B 42 0100 0010C 43 0100 0011a 61 0110 0001b 62 0110 0010c 63 0110 0011


Exercise: More ASCII Practice

What is “01234” (“ means characters) in ASCII?Char Hex Bits0 30 0011 00001 31 0011 00012 32 0011 00103 33 0011 00114 34 0011 0100


ASCII Text Facts

Numbers sort before lettersUppercase letters (ABC) sort before lowercase letters (abc)Numbers represented as 8-bit values are inefficient for storage and arithmetic (12,345 takes 5 x 8 = 40 bits, but binary could store it in fewer bits -– 14 bits)All numbers (0 through 9) start with same bits: 0011


Packed Decimal

All numbers (0..9) start with same bits 0011 With proper encoding/decoding, there is no

need to store the first 4 bits for ASCII number storage

Store only the last (unique) 4 bits of each digit, since first 4 bits for numbers are always the same (0011)

Takes about half the storage spaceWhere is the sign (+/-) stored?


Exercise: Encoding a Number into Packed Decimal

What is “1,234” in ASCII?Char Hex Bits1 31 0011 00012 32 0011 00103 33 0011 00114 34 0011 0100

First 4 bits (0011) are the same for all decimal numbers (0 through 9)Only the low-order 4 bits are stored


Encoding into Packed Decimal…

What is 1,234 in ASCII?Char Hex Bits1 31 0011 00012 32 0011 00103 33 0011 00114 34 0011 0100

Answer: 00010010 00110100


Encoding into Packed Decimal…

What is 1,234 in ASCII?Char Hex Bits1 31 0011 00012 32 0011 00103 33 0011 00114 34 0011 0100

Answer: 00010010 00110100

Now packed into 2 bytes!


Decoding Packed Decimal

Question: What does 00010010 00110100 represent?Someone has to tell you that the bytes contain a number that was stored in packed decimalYou have to decode, then interpret it



Decoding area is createdNumber: 00010010 00110100

0011 0011 0011 0011 4 bytes, with leading 0011 generated in each



Decoding area is loadedNumber: 00010010 00110100

0011 00010001 0011 0011 0011 4 bytes, with leading 0011 generated in each




0011 00010001 0011 00100010 0011 0011 4 bytes, with leading 0011 generated in each




0011 00010001 0011 00100010 0011 00110011 0011 4 bytes, with leading 0011 generated in each




0011 00010001 0011 00100010 0011 00110011 0011 01000100

4 bytes, with leading 0011 generated in each



Decoding area is interpretedNumber: 00010010 00110100

0011 00010001 0011 00100010 0011 00110011 0011 01000100

1 2 3 4


Alternative Number Storages

ASCII text: 8-bit “characters”Packed decimal: 4 bits per digit + signBinary system: base 2 number system Pure binary, positive integers Two’s complement, signed values Excess notation

Floating point: sign-exponent-mantissa


Binary System

Base 2 number systems Pure binary, positive integers Two’s complement, signed values Excess notation

All use bits differently than ASCIINothing in the bits says whether they are binary coding or ASCII


Number Base Basics

The “base” of a number system is defined by how many different digit symbols it usesDecimal is base 10: 0,1,2,3,4,5,6,7,8,9Binary is base 2: 0,1Octal is base 8: 0,1,2,3,4,5,6,7Hex is base 16: 0 thru 9, A,B,C,D,E,F


Number Base Basics …

The “value” of each column in a multi-digit number is determined by the number base it is expressed inExample: What is the decimal value of 1101 in decimal, binary, octal, hex?


Number Base 10 - Decimal

You figure how much each column is worth, starting from the rightmost column:

102 101 100

100’s 10’s 1’s x x x

1 0 1

base2 base1 base0

Base=10(decimal)


102 101 100

100’s 10’s 1’s 1 0 1

Number Base 10 - Decimal

x100

x10

x1 1

0

100

101

1x1

0x10

1x100


22 21 20

4’s 2’s 1’s 1 0 1

Number Base 2 - Binary

x4

x2

x1 1

0

4

5

1x1

0x2

1x4


82 81 80

64’s 8’s 1’s 1 0 1

Number Base 8 - Octal

x64

x8

x1 1

0

64

65

1x1

0x8

1x64


162 161 160

256’s 16’s 1’s 1 0 1

Number Base 16 - Hexadecimal

x256

x16

x1 1

0

256

257

1x1

0x16

1x256


Converting from Base 10 to Other Number Bases

Convert decimal 1,234 to binary - how?Convert decimal 1,234 to hex - how?

Algorithm:1. Divide number by the new number

base2. Record remainder as low order digit3. Replace number with division result

(quotient)4. If quotient is not 0, go back to step 1

and repeat


Example: Converting Decimal 1,234 to Binary

Low-order digit

High-order digit

quotient remainder

1234 / 2 = 617 0617 / 2 = 308 1308 / 2 = 154 0154 / 2 = 77 077 / 2 = 38 138 / 2 = 19 0 1001101001019 / 2 = 9 19 / 2 = 4 14 / 2 = 2 02 / 2 = 1 01 / 2 = 0 1


Example: Converting Decimal 1,234 to Hex

1234 / 16 = 77 277 / 16 = 4 13=D4 / 16 = 0 4

Low-order digit

High-order digit

quotient remainder

4D2


Facts about Binary Numbers

Pure binary system stores positive integers only 8-bit number = 0 to 255 (28) 16-bit number = 0 to 65,535 (216) 32-bit number = 0 to

4,294,967,295 (232)

But no matter how many bits are used, there is always some number too large to be represented


Binary Addition

Binary addition facts

Used as carry


Binary Addition

Addition is as with decimal numbers

1 0 0 1 0 1 0 0

0 1 0 0 1 1 1 0+

1 1 1 0 0 0 1 0

1

1 4 8

7 8

2 2 6

+

decimalbinary

11 1 1


Binary Fractions

Radix point is like decimal point

1 0 1 . 1 0 1

Each column to the right of radix point is worth ½ of column to its left


Binary Fractions


Addition of Binary Fractions

Just like normal binary numbers, add from rightmost to leftmost, use carry ½

¼ 1/8

12

4

= 2 + ¼ + 1/8 = 2.375

= 4 + ½ + ¼ = 4.75

= 7 + 1/8 = 7.1251 1 1. 0 0 1

1 0 0. 1 1 00 1 0. 0 1 1

1 1

+


Exercise: Addition of Binary Fractions

½ ¼ 1/8124

= decimal ?

= decimal ?

= decimal ?

0 1 1 0 1 0 1 0. 0 1 1 1+0 0 1 0 0 0 1 0. 0 1 1 0

? ?

1/168163264128

csc255-702/703 cti/depaul1 csc-255 lecture 3 text and numerical storage (chapter 1 from brookshear)...

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