Data Representation in Computers - Answers

The OCR Specification says that you should be able to:

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

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 •

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

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 •

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

Instructions explain how instructions are coded as bit patterns • explain how the computer distinguishes between instructions and data • Past Paper Exam questions

Jan 2011

1. (a) Calculate the denary value of the 8-bit binary number 10010111. You must show your working.

128 + 16 + 4 + 2 + 1 •

151 •

(b) Add the following two 8-bit binary numbers and explain the result. You must show your working.

Points for:

First nibble correct with carries shown •

Second nibble correct •

There is an overflow because the result > 255/cannot be represented in 8-bits •

2. (a) Explain how ASCII is used to represent text in a computer system.

Each character is given a numeric code

Including symbols, digits, upper and lower case •

This code is then stored in binary •

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)

(b) State what is meant by the character set of a computer.

All the characters which are recognised/can be represented by the computer system

(c) Unicode is also used to represent text in a computer system. Explain the difference between the character sets of Unicode and ASCII.

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.

June 2011

3. (a) Convert the hexadecimal number 6A to denary. You must show your working.

6*16(=96)/10 (forA) •

106 •

(b) Convert the hexadecimal number 6A to binary.

0110 1010 (1 mark per nibble)

(c) Convert the binary number 00111101 to hexadecimal.

3D (1 mark per digit)

(d) Explain why hexadecimal numbers are often used to represent binary numbers.

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.

Jan 2012 4. Bytes, Kilobytes and Megabytes are units used for the amount of data stored in a computer.

(a) State which of these units is most appropriate for the following items of data.

A one page text document:

Kilobyte(s)

A ten minute movie clip:

Megabyte(s)

A person ’s surname:

Byte(s)

(b) A computer has a hard disk of 2 Terabytes. How much is this in Gigabytes?

You must show your working.

Multiply by 1024/1000 •

2048/2000 (GB) •

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.

(a) Tick one box in each row to show whether or not each of the following items must be included in the bitmap file.

(b) (i) What is meant by the resolution of the picture? The concentration of pixels

(ii) How does the resolution affect the size of the bitmap file?

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).

June 2012

6 (a) Convert the denary number 55 to an 8 bit binary number.

0011 0111 (1 mark per nibble)

(b) Convert the denary number 55 to hexadecimal.

37 (1 mark per digit)

Jan 2013

7 (a) Add the following bytes.

Award marks for:

111000 for bits 5 to 0

00 for bits 7 and 6

(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.

8. When recording a sound file on a computer, the sound needs to be sampled.

(i) Describe how sampling is used when storing sound.

The height/amplitude of the sound wave is measured at regular intervals and converted to binary.

(ii) Explain the effect of the sampling interval on the size and quality of the sound file recorded.

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.

9 (a) Explain why data is stored in computers in a binary format.

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.

(b) In the ASCII character set, the character codes for the first three capital letters are given below.

(i) State how the ASCII character set is used to represent text i a computer.

Each character is assigned a unique character code

Each letter is converted to its character code (which is a binary number)

(ii) Convert the word CAB into binary using the ASCII character set.

0100 0011 0100 0001 0100 0010

(iii) Explain why the ASCII character set is not suitable for representing text in all the languages of the world.

ASCII uses 8 bits and so can only represent 255/256 distinct characters. •

Many more characters are needed for coping with all languages (eg Unicode 16bits). • ASCII does contain characters used in some languages •