How many bits per pixel would be required for an …



ANSWERS:LESSON 1Questions:Binary is a number system that only uses two digits: 1 and 0.?All information that is processed by a computer is in the form of a sequence of 1s and 0s. Therefore, all data that we want a computer to process needs to be converted into binary.Denary0000011Base 2401702564130left00LESSON 2 Binary AdditionQuestions 02095500Lesson 3 Binary Subtraction0067500519748500left000Lesson 4 Binary addition and subtractionright37528500Lesson 5: An Introduction To Hexadecimalsleft30734000Lesson 6 Hexadecimalleft2349500Lesson 7 Sign MagnitudeLesson 8 Two’s Complement3100011111Complement11100000-31111000016601000010Complement10111101-661011111010001100100 Complement10011011-10010011100Convert the negative two’s complement number back to positive:-511111011Complement00000100500000101-4411010100Complement001010114400101100left152400 5715050717450-85725285750Lesson 9 Sign Magnitude and Two’s complement continueLESSON 10 Exam QuestionsTASK 1:1 (i) - 0011 1100(ii) - 35(iii) 0110 1101-9048711918953)003)-635101602)002)-176213838205)005)-285753857631001Lesson 11 Exam Questions Continued-76200841372002left6350400438100114305005-1381123228986006The answers to the 8-bit binary addition problems are listed below. 010011102?+?001111002??=??100010102100111012?+?100011112??=??1001011002110100112?+?010101102??=??1001010012100100112?+?101110012??=??1010011002111111102?+?101101012??=??1101100112101111012?+?111001112??=??1101001002The binary answers are listed below.110010102?-?100110102??=??001100002 100111002?-?011110012??=??001000112 110010112?-?100000112??=??010010002 111000012?-?100111012??=??010001002 100000012?-?011001102??=??000110112 100100112?-?100001112??=??000011002 Lesson 12 Binary ImagesGraded exercises answersHow many bits per pixel would be required for an image with a palette of 256 possible colours? [1]8State two factors that affect the file size of a bitmap image.[2]Colour depth / number of bits per pixel / number of colours in the imageDimensions of the image in pixels / resolution - ‘Size of the image’ is not enoughAdditional metadata data is stored alongside the binary colour values for each pixel. Give two examples of metadata.[2]Answers include: Dimensions / Width and heightBit depth / colour depth / number of bits per pixelFile nameDate created / modifiedFile typeAuthorCalculate the file size of the following images:Image ResolutionNumber of coloursColour depth in bitsFile size in bitsFile size in BytesImage 120 x 20831,200150Image 210 x 108330037.5Image 320 x 2042800100How does increasing the image resolution affect the file size?Increasing the resolution will increase the number of pixels used, therefore increasing the file size since each additional pixel will require extra binary data to store its colour value.Explain the relationship between image quality and file sizeAs the number of pixels increases in the same area, the quality improves, as does the file size. As the number of colours in an image increases, the data required to store a greater number of colours increases, as does the quality and the file size.B gradeLine numberBinary image data100001110-11011010200001110-11011010300001010-11011010, 00000001-10100101, 00000011-11011010400001001-11011010, 00000011-10100101, 00000010-11011010500001000-11011010, 00000101-10100101, 00000001-11011010Lesson 13 SoundWorksheet 4: Sampling sound AnswersLook at the sound wave below and record the samples in the table beneath it. The first two are done for you. You can only plot a sample at an intersection. Use a ‘best-fit’ approach.012345678910111213146811139.53.5313.823.16.574.578.215161718192021222324252627282932.813137.51.51.366.55.38.58.15.5212.7(n.b. There is some margin for error in each of these points!)Replot all of your figures on to the graph below and create a bar chart from the points. The first two points have been drawn for you. How accurately does this represent the original sound wave? Where are there inaccuracies in the digital reproduction of the wave? The wave is reproduced with reasonable accuracy, to the point that you might actually recognise the tune (albeit in poorer quality) if this were a real practical example. The peaks and troughs of the wave are not represented accurately in the reconstructed drawing.What would you need to do in order to improve the accuracy of the recording?Take samples more frequently and increase the number of points on the Y axis at which you can record a pleted graph:In reality, each of the measurements on the Y axis would be given a binary value and that would be recorded in the audio data file. Using Table 1 below write out the binary values for each of the first ten samples given in Table 2. There are 16 sampling points on the Y axis so a minimum of four bits must be used in order to provide enough different bit patterns for each sampling point.YBit value100012001030011401005010160110701118100091001101010111011121100131101141110151111Table 1Sample0123456789Value68111310461424Binary value0110100010111101101001000110111000100100Table 2The Binary Values in the third row above represent the data that would be stored to recreate this very short sound file of 10 samples.What would be the file size in bytes of the 10 samples in Question 5?10 samples, each using 4 bits = 40 bits / 8 = 5 bytesThe resolution is the accuracy with which the wave height is measured – the higher the resolution, the more accurate the measurement at a particular sample point. What would the file size of samples in question 3 become if you increased the resolution to allow for 256 different points on the Y axis? 256 points would require 8 bits. 8 x 10 = 80 bits or 10 bytes.How would this affect the quality of the recording?The recording quality would increase since the wave height with each sample could be recorded 16 times more accurately.The sampling frequency is the frequency with which the measurements are taken – a higher sampling frequency means measurements are taken more often within the same period of time. How would this affect the quality of the recording?The more often you are able to sample, the more accurately you can record changes in the wave height, and therefore the more accurately you can reproduce the recording digitally to create a higher quality output.Explain the relationship between the quality of playback and the file size.As quality of playback increases, owing to a greater number of samples or a greater sampling accuracy, the more data is generated, and therefore the larger the sound file.KEY WORDS – BinaryBase 2 numbers. Only digits ‘1’ and ‘0’ are allowed.BitThe smallest unit of data – a bit can take the value of ‘0’or ‘1’, alternatively expressed as ‘false’ or ‘true’.NibbleHalf of a byte – 4 bitsByteThe smallest addressable unit of data in a computer. Usually 8 bits.Gigabyte (GB)1024 megabytesKilobyte (kB)1024 bytesMegabyte (MB)1024 kilobytesNibbleHalf a byteTerabyte (TB)1024 gigabytesBinaryNumbers expressed in base 2.Decimal (denary)Numbers expressed in base 10.HexadecimalNumbers expressed in base 16.OverflowAn error caused by attempting to store a number that is too large for the number of bits available.MetadataFor the computer to interpret an image file and rebuild the picture it must know some other things about this data file.Sign Magnitude Two’s ComplementTwo methods of representing negative numbers using binarySample rateSample rate?is the number of samples recorded in any given period of time. The higher the sample rate, the closer the recorded signal is to the original. Bit depthBit rate refers to the number of?bits?used to record each sample. Bit rateBit rate?is a measure of how much data is processed for each second of sound. Bit rate is calculated by: Sample rate × bit depth ................
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