<p>Data Representation in Computers - Answers</p><p>The OCR Specification says that you should be able to:</p><p>Units define the terms bit, nibble, byte, kilobyte, megabyte, gigabyte, terabyte • understand that data needs to be converted into a binary format to be processed by a • computer</p><p>Numbers convert positive denary whole numbers (0-255) into 8-bit binary numbers and vice versa • add two 8-bit binary integers and explain overflow errors which may occur • convert positive denary integers (0-255) into 2-digit hexadecimal numbers and vice versa • convert between binary and hexadecimal equivalents of the same number • explain the use of hexadecimal numbers to represent binary numbers •</p><p>Characters explain the use of binary codes to represent characters • explain the term character set • describe with examples (for example ASCII and Unicode) the relationship between the • number of bits per character in a character set and the number of characters which can be represented</p><p>Images explain the representation of an image as a series of pixels represented in binary • explain the need for metadata to be included in the file such as height, width and colour • depth discuss the effect of colour depth and resolution on the size of an image file •</p><p>Sound explain how sound can be sampled and stored in digital form • explain how sampling intervals and other considerations affect the size of a sound file • and the quality of its playback</p><p>Instructions explain how instructions are coded as bit patterns • explain how the computer distinguishes between instructions and data • Past Paper Exam questions</p><p>Jan 2011</p><p>1. (a) Calculate the denary value of the 8-bit binary number 10010111. You must show your working.</p><p>128 + 16 + 4 + 2 + 1 •</p><p>151 •</p><p>[2] </p><p>(b) Add the following two 8-bit binary numbers and explain the result. You must show your working.</p><p>Points for:</p><p>First nibble correct with carries shown •</p><p>Second nibble correct •</p><p>There is an overflow because the result > 255/cannot be represented in 8-bits •</p><p>[3] </p><p>2. (a) Explain how ASCII is used to represent text in a computer system.</p><p>Each character is given a numeric code</p><p>Including symbols, digits, upper and lower case •</p><p>This code is then stored in binary •</p><p>Each character takes 1 byte • Text is stored as a series of bytes (1 per character)  Some codes are reserved for • control characters (eg TAB, Carriage Return)</p><p>[3] </p><p>(b) State what is meant by the character set of a computer. </p><p>All the characters which are recognised/can be represented by the computer system</p><p>[1] </p><p>(c) Unicode is also used to represent text in a computer system. Explain the difference between the character sets of Unicode and ASCII.</p><p>Unicode has a much larger character set and can represent many more characters/characters from all alphabets, because unicode uses 16 bits and ASCII uses fewer/7/8 bits.</p><p>[2]</p><p>June 2011</p><p>3. (a) Convert the hexadecimal number 6A to denary. You must show your working.</p><p>6*16(=96)/10 (forA) •</p><p>106 •</p><p>[2]</p><p>(b) Convert the hexadecimal number 6A to binary. </p><p>0110 1010 (1 mark per nibble)</p><p>[2]</p><p>(c) Convert the binary number 00111101 to hexadecimal. </p><p>3D (1 mark per digit)</p><p>[2]</p><p>(d) Explain why hexadecimal numbers are often used to represent binary numbers. </p><p>Hex numbers are shorter/more memorable than equivalent binary numbers and can easily be converted to and from binary as each hex digit corresponds to 4 binary digits. A diagram will be accepted.</p><p>[2] </p><p>Jan 2012 4. Bytes, Kilobytes and Megabytes are units used for the amount of data stored in a computer. </p><p>(a) State which of these units is most appropriate for the following items of data.</p><p>A one page text document: </p><p>Kilobyte(s) </p><p>A ten minute movie clip: </p><p>Megabyte(s)</p><p>A person ’s surname: </p><p>Byte(s)</p><p>[3] </p><p>(b) A computer has a hard disk of 2 Terabytes. How much is this in Gigabytes? </p><p>You must show your working.</p><p>Multiply by 1024/1000 •</p><p>2048/2000 (GB) •</p><p>[2]</p><p>5. Peter takes a picture of himself and his friends to put on a social networking site. The picture is converted into pixels and stored as a bitmap file.</p><p>(a) Tick one box in each row to show whether or not each of the following items must be included in the bitmap file.</p><p>[5]</p><p>(b) (i) What is meant by the resolution of the picture? The concentration of pixels</p><p>[1]</p><p>(ii) How does the resolution affect the size of the bitmap file?</p><p>2 (The higher the resolution) more pixels are required for the picture which will increase the size of the bitmap file. (Accept lower resolution fewer pixels, smaller size).</p><p>[2]</p><p>June 2012</p><p>6 (a) Convert the denary number 55 to an 8 bit binary number. </p><p>0011 0111 (1 mark per nibble)</p><p>[2] </p><p>(b) Convert the denary number 55 to hexadecimal. </p><p>37 (1 mark per digit)</p><p>[2]</p><p>Jan 2013</p><p>7 (a) Add the following bytes.</p><p>Award marks for:</p><p>111000 for bits 5 to 0 </p><p>00 for bits 7 and 6</p><p>[2]</p><p>(b) State the problem that will occur if a computer is to store the result as a byte. 1 There is an overflow/a carry left over after the addition/does not fit into one byte.</p><p>[1]</p><p>8. When recording a sound file on a computer, the sound needs to be sampled.</p><p>(i) Describe how sampling is used when storing sound. </p><p>The height/amplitude of the sound wave is measured at regular intervals and converted to binary. </p><p>[2] </p><p>(ii) Explain the effect of the sampling interval on the size and quality of the sound file recorded. </p><p>If the interval is smaller/if you sample more often you have more data to store so a larger file but the sound reproduced is closer to the original so better quality. </p><p>[3] </p><p>9 (a) Explain why data is stored in computers in a binary format.</p><p>Circuit only needs to check for two states/uses switches. Electricity flowing or not flowing/on or off/1 and 0 resulting in more reliable circuits.</p><p>[2]</p><p>(b) In the ASCII character set, the character codes for the first three capital letters are given below.</p><p>(i) State how the ASCII character set is used to represent text i a computer. </p><p>Each character is assigned a unique character code</p><p>Each letter is converted to its character code (which is a binary number) </p><p>[1] </p><p>(ii) Convert the word CAB into binary using the ASCII character set.</p><p>0100 0011 0100 0001 0100 0010</p><p>[1] </p><p>(iii) Explain why the ASCII character set is not suitable for representing text in all the languages of the world.</p><p>ASCII uses 8 bits and so can only represent 255/256 distinct characters. •</p><p>Many more characters are needed for coping with all languages (eg Unicode 16bits). • ASCII does contain characters used in some languages •</p><p>[2]</p>