Unit 1.1: Information representation

Transcription

1 Unit 1.1: Information representation Different number system A number system is a writing system for expressing numbers, that is, a mathematical notation for representing numbers of a given set, using digits or other symbols in a consistent manner. The simplest number system is a unary number system, in which every natural number is represented by a corresponding number of symbols. e.g: if symbol chosen is then 5 is represented by Positional notation The value of each digit is represented by which place it appears in the full number. The lowest place value is the rightmost position and each successive position to the left has a higher place value. The value of each position corresponds to the power of the base of the number system. Few number systems Binary number system: Numbers are expressed with base 2, using two different symbols: 0 & 1. Decimal number system: Numbers are expressed with base 10. Valid values are from 0 to 9. Hexadecimal number system: Numbers are represented with base 16, using16 distinct symbols 0 9 to represent values zero to nine, & A, B, C, D, E, F to represent 10 to 15. Convert a number from one number system to another Decimal to other base systems Step1: ivied the decimal number to be converted by the value of new base Step2: get the remainder from step1 as the right most digit of new base number Step3: divide the quotient of the previous divide by the new base. Step4: Record the remainder from step 3 as the next digit (to the left) of the new base number. Repeat steps 3 & 4, getting remainders from right to left until the quotient becomes zero in step 3. The last remainder thus obtained will be the MSB of the new base number.

2 e.g: (75) 10 into Binary =( ) 2 (175) 10 into Hex (F) 0 10(A) =(AF) 16 Others to Decimal Step1: Determine the column value of each digit Step2: multiply the obtained column values by the digits in the corresponding columns Step3: sum the products calculated in step2. The total is the equivalent value in decimal. e.g: (11101) 2 into decimal =1*24 + 1* * * *20 = =(29) 10 (A1B) into Decimal =A*162 +1*161+B*160 =10* = =(2587) 10 Representation of numbers using 2 s complement form Lets have a look at Sign and Magnitude method before proceeding to 2 s complement method. The first bit in the byte i.e. the most significant bit (MSB) will represent the sign. 0 represents positive and 1 represents negative. This means that:

3 +117= and 117= Now let s check for 2 s complement method. The following algorithm is another way of calculating the 2 s complement value of a negative number: Workout the binary value of the positive number (make sure you write down all the leading zeros) Change all the digits, 0 for 1 and 1 for 0. Add 1. e.g: ( 117) 10 into binary +117= s = s = = e.g: = x2= x2= = S= S: = e.g: = S= S: = e.g: = ( )2 e.g: = S= S= =

4 e.g: = e.g: 9 +9= S= S: = e.g: = X2=1 = e.g: = S= S: = Character representation in binary using ASCII ASCII(American standard code for information interchange) originally used 7 bit code that could represent 128 different character including letters, number &special symbols. Letter 8 th bit was also used to allow an extra 128 characters to be represented.there are known as extended ASCII Character ASCII code Binary(7/8bits) A , Express a denary number in BCD & vice versa In BCD system each decimal digit is represented by its own 4 bit binary code Eg 3765=

5 Describe practical applications where BCD is used BCD arithmetic is used in business applications where thy eliminate the problems of reading erross inherit in using floating point numbers mostly used in financial commercial & industrial computing where fractiond reading erross can not be tolerated Images Show understanding of how data for a bitmapped image is encoded. A digital image is composed of pixels arranged in a rectangles array with certain height and width. A bitmap is characterized by the width and height of the image in pixels, the no of bits per pixel, which determines the number of shades of grey, or colors it can represent. A monochrome screen will read just one bit in memory to represent each pixel; if the bit is 1, the pixel is on, & if it is 0, the pixel is off. On a color screen each pixel may correspond to one byte in memory giving a possible 256 colors for each pixel. Two bytes per pixel give possible 64k different colors. A 24 bit bitmap will use one byte each for red, blue & green 16 colors each pixel four bits Terminologies associated with bitmaps pixel : It is smallest unit of an image. It is referred to as the smallest resolvable area of an image, the smallest element of an image, which can be individually processed in a video display system. File header: It is small amount of data at the beginning of a file. It varies between file formats, but they generally define the content of the file and list specific file attributes. For e.g: the header of image file may include image format, color profile and application that created the file. Image resolution: this term is often used for a pixel count in image. The smaller the size of pixel, the higher the resolution will be. Images having smaller pixel sizes occupy more space on the disk. Screen resolution: The number of horizontal and vertical pixels on a display screen. The more pixels, the more information is visible without scrolling. 1) 100 x 100 pixels & 24 bit color used, then total memory required is, 24 bits = 3 bytes/pixel 100 x 100 = 3 x = bytes in total

6 Vector graphics Vector graphics store set of instructions for drawing geometric sets, like co ordinate points, shapes, color, etc. Vector graphics can be resized by any amount without losing quality, i.e. it is resolution independent. It take up less storage space than bitmap (raster images), but require more processing power to repeatedly redraw the image. Drawing objects: These are individual element of which vector images are made up of. These objects can be lines, curves, circles, rectangles or any other shape connected by paths and points. Drawing list: in vector graphic format, object information is stored in drawing list file. Properties: Each instruction in the drawing list lists the properties of the object being drawn, the thickness of a line, coordinates, font size, brush style, border color. Justify where bitmapped graphic and vector graphics are appropriate for a given task Vector graphic are suitable for fonts logos clipart Raster graphics are suitable of Realistic images Digital photographs sound Show understanding of how sound is represented & encoded Sound is an analogue physical quantity that varies with time, these have to be converted into digital format. In particular, samples of the sound will have to be taken, & each sample will have to be quantized to the nearest binary code in digital representation Concept of frequency of sound Sound consists air vibrations, and it is the rate at which the air vibrates at, say,100 cycles per second then the frequency of sound is 100hz 1 unit for cycle per second stands for hertz. Sampling Sampling is reduction of continuous signal to a discrete signal. In terms of sound wave samples are stored as numbers, referring to the height of the wave at that point

7 Sampling rate It is how many sound wave samples are taken per second, not to miss any meaningful changes in the original signal So how often the sound must be sampled? This rule is called the sampling theorem which says that if the frequencies in the sound range from 0 to B Hz then, fir a faithful representation, the sound must be sampled at rate greater then 2B samples per second Sample resolution A more accurate representation o f the analog signal can be achieved if more bits are used to store each sample. 5 minutes of music is sampled at samples per second,& each sample is encoded into 16 bits(2bytes). How big will the resulting music file be? 5 minutes =300 seconds So, no of samples A. =300*40000 Bikash 1 sample =2 bytes 300*40000 sample =300*40000*2= bytes =Approx. 24 MB Sound editing Representing sound in digital from allows for editing this might mean removing background noise or specific frequencies. It might mean cropping or merging with other sounds : Video show the understanding of the characteristics of video streams Video is simply a series of still images presented at sufficiently short time intervals that the edge smoothes over the change from one image to the next Frame Each still image that goes to make up a moving image is known as frame. FRAME RATE: The number of still pictures per unit of time of video is called frame rate. The minimum frame rate to achieve a comfortable illusion of a moving image is about sixteen frames/second. Interlaced & progressive encoding Interlaced encoding was the way to reduce flicker without increasing the number of complete frames per second in early mechanical & CRT video displays.

8 In progressive systems, each refresh periods updates all scan lines in each frame in sequence that results in optimum special resolution of both the stationary & moving parts of the image. Such encoding is useful for devices like LCD television, digital video projector or plasma panel. Video interframe compressionalgorithms & special & temporal redundancy Spatial redundancy: This refers to the correction between neighboring pixels. It refers to the pixels in an image having same detail. Temporal redundancy: Pixels in two video frames, which have the same values in the same location. Video interframe compression: This compression technique tries to take advantage from temporal redundancy between neighboring frames to achieve higher compression rates. Algorithm: An frame is divided into blocks known as macro blocks The encoder will try to find a block in other frames on the basis of reference block If the encoder A. succeeds Bikash on its search, the block could be encoded by a vector known as motion vector, which points to the position of the matching block at the reference frame. However the block found may not exactly match, in that case, the difference known as prediction error is computed. with the help of motion vector and prediction error, the decoder will be able to recover the raw pixels of the block. Multimedia container formats It is a digital file format that holds audio, video & subtitles. Container supports a variety of audio & video compression methods and not tied to one particular audio or video codec. AVI was the first container format Compression Techniques Lossless Compression: It recreates a file as an identical match to its original form. All lossless compression uses techniques to breakup a file into smaller segments, for storage and transmission, that gets reassembled later. E.g: Zip file.

9 Lossy Compression: It eliminates repeated pieces of data. A lossy data compression method is one where compressing data & then decompressing it retrieves data that may well be different from the original, but is close enough to be useful in some way. Runtime encoding: The runtime requirements for encoding substantially depends on the desired usage. e.g: live broadcasting, fax messaging. In video broadcasting, both audio & video signals must be coupled before broadcasting, without exceeding a specific delay time. While sending fax, the consecutive occurrences of a given symbol are replaced with one copy symbol along with a count of how many times that symbol occurs.