1

Information Representation

2

Computer Architecture

Memory

• Memory is a collection of cells, each with a unique physical address for random (direct) access

• memory is divided into fixed-length units or words

• Information that is stored in memory cells is in binary coded format:

– Instructions that make up programs

– Data: text symbols, numbers, images, etc.

4

Information Representation

• The Binary System: Using On/Off Electrical States to Represent Data & Instructions

• The binary system has only two digits--0 and 1.

• Bit - binary digit

• Byte - group of 8 bits used to represent one character, digit, or other value

5

Representing Information withBit Combinations

• To encode entities (e.g., symbols), we need to assign a unique number to each entity (e.g., social security number). Binary encoding means that we assign a unique combinations of bits to each object.

• One bit can be either 0 or 1. Therefore, one bit can represent only two things.

• To represent more than two things, we need multiple bits. Two bits can represent four things because there are four combinations of 0 and 1 that can be made from two bits: 00, 01, 10,11.

• If we want to represent more than four things, we need more than two bits. In general, 2n bits can represent 2n things because there are 2n combinations of 0 and 1 that can be made from n bits.

• Q: how many bits do we need to encode all the 37 people in the class?

6

Information Representation

• Kilobyte approx. 1000 bytes (actually 210 = 1024 bytes)

• Megabyte approx. 1,000,000 bytes (one million)

• Gigabyte approx. 1,000,000,000 bytes (one billion)

• Terabyte approx. 1 trillion bytes

• Petabyte approx. 1 quadrillion bytes

7

Representing Text and Symbols

• To represent a text document in digital form, we simply need to be able to represent every possible character that may appear.

• There are finite number of characters to represent. So the general approach for representing characters is to list them all and assign each a number (represented in binary).

• An encoding scheme is simply a list of characters and the codes used to represent each one.

• To represent symbols, computers must use a standard encoding scheme, so that the same symbols have the same codes across different computers.

8

ASCII Encoding Scheme

• ASCII stands for American Standard Code for Information Interchange. The ASCII character set originally uses 8 bits to represent each character, allowing for 256 (or 28) unique characters.

9

Representing Text and Symbols

• ASCII - the binary code most widely used with microcomputers

• EBCDIC - used with large computers

• Unicode - uses two bytes for each character rather than one

10

The Parity Bit

• Even parity - sum of bits must come out even

– Ex: given code 01010101, the extended code is: 010101010

– Ex: given code 01101101, the extended code is: 011011011

• Odd parity - sum of bits must come out odd

Even parity scheme

Parity bit - an extra bit attached to the end of a byte for purposes of checking for accuracy

11

Representing Numbers

The binary number system

• Decimal is base 10: 0,1,2,3,4,5,6,7,8,9• Binary is base 2: 0,1

• Any decimal number can be converted to binary by doing base conversion from base 10 to base 2.

• Any binary number can be converted to decimal by doing base conversion from base 2 to base 10.

12

Number base 10 - decimal

• 102 101 100

• 100’s 10’s 1’s• 1 0 1• x 1 = 1• x10 = 0• x100 = 100• 101

The Decimal Number 101

13

Number base 2 - binary

• 22 21 20

• 4’s 2’s 1’s• 1 0 1• x 1 = 1• x 2 = 0• x 4 = 4• 5

The Binary Number 101

14

Binary Conversion - Examples

1 0 1 1 0 1

202122232425

1 2 4 81632

32 + 0 + 8 + 4 + 0 + 1 = 45

15

Binary Conversion - Examples

1 0 1 0 1 1 0

1 2 4 81632 64 + 0 + 16 + 0 + 4 + 2 + 0 = 8664

Easier way to remember:Just add the values for each position where there is a 1

1 0 1 1 0 1 0 1

2 4 8163264 1128

128 + 32 + 16 + 4 + 1 = 181

16

Hexadecimal Representation

• Hexadecimal (Hex) = Base 16– Hex digits: 0, 1, 2, …, 9, A, B, C, D, E, F

Decimal

Hex Binary

8 8 1000

9 9 1001

10 A 1010

11 B 1011

12 C 1100

13 D 1101

14 E 1110

15 F 1111

Decimal

Hex Binary

0 0 0000

1 1 0001

2 2 0010

3 3 0011

4 4 0100

5 5 0101

6 6 0110

7 7 0111

17

Hexadecimal Representation

• Hex can be used as a short hand for long binary strings– Use one Hex digit to represent every group of 4 bits– Start from the right and an go left grouping 4 bit sequences– Add leading 0’s if the last group has less then 4 bits

1 0 1 0 1 1 0 1 0 1 1 0 1 0 1 0 1 1 0 1 0 1 1 0

A D 6

1 0 1 1 0 1 1 0 1 0 1 1 0 1 1

5 B

18

Hexadecimal Representation

• What is Hex 4C8F in binary?

4 C 8 F

1111100011000100

19

Representing Images as Bit maps

• Image is collection of dots (pixels)• Pixel = “picture element”

– Black & white: one bit per pixel– Color: each pixel represented by combination of green, red, blue in varying

intensity, to form all colors. Three bytes per pixel: one byte (8 bits) for each color intensity, 0-255 value

– Usually each byte is represented in Hex D4 7F 59 red (D4), green (7F), blue (59) For example, D4 is binary 1101 0100 which is decimal value 212

• Bit maps are not efficient– 3 byte/pixel, for 1280 x 1024 pixels = several megabytes– Image cannot be enlarged, since pixels get bigger and image gets grainy or

“blocky”– .GIF and .JPEG formats compress images

20

Image Formats

• GIF– Graphics Interchange Format– Developed by Compuserve (ISP)– Stores only 256 colors– Loses some picture quality but is simple and fast– Common in computer action games

• JPEG (JPG)– Joint Photographic Experts Group– Stores differences between adjacent pixels, not absolute

values– Uses variable-length data (values take a minimum number

of bits to store), uses only 5% of the space of bitmaps

21

Image Formats

• Vector Images– Pixels are not mapped– Equations for the lines and curves making up the image are stored– Image is stored as the instructions for drawing the image– Images are easily scaled– Modern type fonts are vector images– Used in computer aided design (CAD) systems for “blueprint”

drawings– Good for three-dimensional drawings– Windows metafile (.wmf) or Visio (.vsd)– Cannot produce photographic images