DATA REPRESENTATION

Data Representation refers to the methods used internally to represent information stored in a computer. Computers store lots of different types of information:

1. numbers.
2. text.
3. graphics of many varieties (stills, video, animation).
4. sound.

Computers use numeric codes to represent all the information they store. These codes are similar to those you may have used as a child to encrypt secret notes: let 1 stand for A, 2 stand for B, etc. With this code, any written message can be represented numerically. The codes used by computers are a bit more sophisticated, and they are based on the binary number system (base two) instead of the more familiar decimal system. Computers use a variety of different codes. Some are used for numbers, others for text, and still others for sound and graphics.

 

MEMORY STRUCTURE IN COMPUTER

1. Memory consists of bits (0 or 1). A single bit can represent two pieces of information.
2. Bytes (= 8 bits). A single byte can represent 256 = 2x2x2x2x2x2x2x2 = 2ˆ8 pieces of information.
3. Words (= 2,4, or 8 bytes). A 2 byte word can represent 256² pieces of information (approximately 65 thousand).
4. Byte addressable – each byte has its own address.

 

BINARY NUMBERS

Normally we write numbers using digits 0 to 9. This is called base 10. However, any positive integer (whole number) can be easily represented by a sequence of 0’s and l’s. Numbers in this form are said to be in base 2 and they are called binary numbers. Base 10 numbers use a positional system based on powers of 10 to indicate their value. The number 123 is really 1 hundred + 2 tens + 3 ones. The value of each position is determined by ever-higher powers of 10, read from left to right. Base 2 works the same way, just with different powers. The number 101 in base 2 is really 1 four + 0 twos + 1 one (which equals 5 in base 10).

(a) Text: Text can be represented easily by assigning a unique numeric value for each symbol used in the text. For example, the widely used ASCII code (American Standard Code for Information Interchange) defines 128 different symbols (all the characters found on a standard keyboard, plus a few extra), and assigns to each a unique numeric code between 0 and 127. In ASCII, an “A” is 65,” B” is 66, “a” is 97, “b” is 98, and so forth. When you save a file as “plain text”, it is stored using ASCII. ASCII format uses 1 byte per character 1 byte gives only 256 (128 standard and 128 non-standard) possible characters The code value for any character can be converted to base 2, so any written message made up of ASCII characters can be converted to a string of 0’s and 1’s.

 

(b) Graphics: Graphics that are displayed on a computer screen consist of pixels: the tiny “dots” of color that collectively “paint” a graphic image on a computer screen. The pixels are organized into many rows on the screen. In one common configuration, each row is 640 pixels long, and there are 480 such rows. Another configuration (and the one used on the screens in the lab) is 800 pixels per row with 600 rows, which is referred to as a “resolution of 800×600.” Each pixel has two properties: its location on the screen and its color.

A graphic image can be represented by a list of pixels. Imagine all the rows of pixels on the screen laid out end to end in one long row. This gives the pixel list, and a pixel’s location in the list corresponds to its position on the screen. A pixel’s color is represented by a binary code, and consists of a certain number of bits. In a monochrome (black and white) image, only 1 bit is needed per pixel: 0 for black, 1 for white, for example. A 16 color image requires 4 bits per pixel. Modern display hardware allows for 24 bits per pixel, which provides an astounding array of 16.7 million possible colors for each pixel.

 

(c) Compression: Files today are so information-rich that they have become very large. This is particularly true of graphics files. With so many pixels in the list, and so many bits per pixel, a graphic file can easily take up over a megabyte of storage. Files containing large software applications can require 50 megabytes or more! This causes two problems: it becomes costly to store the files (requires many floppy disks or excessive room on a hard drive), and it becomes costly to transmit these files over networks and phone lines because the transmission takes a long time. In addition to studying how various types of data are represented, you will have the opportunity today to look at a technique known as data compression. The basic idea of compression is to make a file shorter by removing redundancies (repeated patterns of bits) from it. This shortened file must of course be de-compressed – have its redundancies put back in – in order to be used. However, it can be stored or transmitted in its shorter compressed form, saving both time and money.

 

BINARY CODED DECIMAL (BCD)

Binary coded decimal (BCD) is a system of writing numerals that assigns a four-digit binary code to each digit 0 through 9 in a decimal (base10) numeral. The four-bit BCD code for any particular single base-10 digit is its representation in binary notation, as follows:

0 = 0000

1 = 0001

2 = 0010

3 = 0011

4 = 0100

5 = 0101

6 = 0110

7 = 0111

8 = 1000

9 = 1001

Numbers larger than 9, having two or more digits in the decimal system, are expressed digit by digit. For example, the BCD rendition of the base-10 number 1895 is 0001 1000 1001 0101

The binary equivalents of 1, 8, 9, and 5, always in a four-digit format, go from left to right.

The BCD representation of a number is not the same, in general, as its simple binary representation. In binary form, for example, the decimal quantity 1895 appears as 11101100111.

Other bit patterns are sometimes used in BCD format to represent special characters relevant to a particular system, such as sign (positive or negative), error condition, or overflow condition.

The BCD system offers relative ease of conversion between machine-readable and human-readable numerals. As compared to the simple binary system, however, BCD increases the circuit complexity. The BCD system is not as widely used today as it was a few decades ago, although some systems still employ BCD in financial applications.

 

EBCDIC

EBCDIC is an acronym for Extended Binary Coded Decimal Interchange Code. It is a binary code for alphabetic and numeric characters that IBM developed for its larger operating systems. It is the code for text files that is used in IBM’s OS/390 operating system for its S/390 servers and that thousands of corporations use for their legacy applications and databases. In an EBCDIC file, each alphabetic or numeric character is represented with an 8-bit binary number (a string of eight 0’s or 1’s). 256 possible characters (letters of the alphabet, numerals, and special characters) are defined. IBM’s PC and workstation operating systems do not use IBM’s proprietary EBCDIC. Instead, they use the industry standard code for text, ASCII. Conversion programs allow different operating systems to change a file from one code to another.

 

ASCII

ASCII is an acronym for American Standard Code for Information Interchange. It is the most common format for text files in computers and on the Internet. In an ASCII file, each alphabetic, numeric, or special character is represented with a 7-bit binary number (a string of seven Os or 1s). 128 possible characters are defined.

ASCII codes table – Format of standard characters.