Data Representation in Computers - Answers

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

[2]

(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

[3]

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)

[3]

(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

[1]

(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.

[2]

June 2011

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

• 6*16(=96)/10 (forA)

• 106

[2]

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

0110 1010
(1 mark per nibble)

[2]

3D
(1 mark per digit)

[2]

(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.

[2]

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)

[3]

(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)

[2]

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.

[5]

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

The concentration of pixels

[1]

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

(The higher the resolution) more pixels are required 2 for the picture which will increase the size of the bitmap file. (Accept lower resolutionfewer pixels, smaller size).

[2]

June 2012

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

0011 0111
(1 mark per nibble)

[2]

(b) Convert the denary number 55 to hexadecimal.

37
(1 mark per digit)

[2]

Jan 2013

7 (a) Add the following bytes.

Award marks for:

111000 for bits 5 to 0

00 for bits 7 and 6

[2]

(b) State the problem that will occur if a computer is to store the result as a byte.

There is an overflow/a carry left over after the addition/does not fit into 1 one byte.

[1]

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.

[2]

(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 filebut the sound reproduced is closer to the original so better quality.

[3]

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.

[2]

(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)

[1]

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

0100 0011 0100 0001 0100 0010

[1]

(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

[2]