Information Representation

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.

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

Representing Information with Bit 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?

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 FACTOIDs: The prefix “mega” in “megabyte” comes from the Greek word “megas” meaning “mighty” or “great.” The prefix “giga” in “gigabyte” comes from a Greek word meaning “giant.” The prefix “tera” in “terabyte” comes from a Greek word meaning “monster.” You might think that the largest unit of storage capacity is a petabyte, but in fact, there are also exabytes, zetabytes, and yottabytes.

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. Discussion question: How many possible different characters can Unicode represent and how is that derived? Answer: 2 to the 16th power=65,526 character combinations

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. Discussion question: How many possible different characters can Unicode represent and how is that derived? Answer: 2 to the 16th power=65,526 character combinations

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 Discussion question: How many possible different characters can Unicode represent and how is that derived? Answer: 2 to the 16th power=65,526 character combinations

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

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.

Number base 10 - decimal The Decimal Number 101 102 101 100 102 101 100 100’s 10’s 1’s 1 0 1 x 1 = 1 x10 = 0 x100 = 100 101

Number base 2 - binary The Binary Number 101 22 21 20 4’s 2’s 1’s 22 21 20 4’s 2’s 1’s 1 0 1 x 1 = 1 x 2 = 0 x 4 = 4 5

Binary Conversion - Examples 1 0 1 1 0 1 32 + 0 + 8 + 4 + 0 + 1 = 45 25 24 23 22 21 20 32 16 8 4 2 1

Binary Conversion - Examples 1 0 1 0 1 1 0 64 + 0 + 16 + 0 + 4 + 2 + 0 = 86 64 32 16 8 4 2 1 Easier way to remember: Just add the values for each position where there is a 1 128 64 32 16 8 4 2 1 1 128 + 32 + 16 + 4 + 1 = 181

Hexadecimal Representation Hexadecimal (Hex) = Base 16 Hex digits: 0, 1, 2, …, 9, A, B, C, D, E, F Decimal Hex Binary 0000 1 0001 2 0010 3 0011 4 0100 5 0101 6 0110 7 0111 Decimal Hex Binary 8 1000 9 1001 10 A 1010 11 B 1011 12 C 1100 13 D 1101 14 E 1110 15 F 1111

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

Hexadecimal Representation What is Hex 4C8F in binary? 4 C 8 F 0100 1100 1000 1111

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

Image Formats GIF JPEG (JPG) 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

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