1.1 Data Representation
AS Level · 26 questions found
What this topic covers
Section titled “What this topic covers”- Binary prefixes vs decimal prefixes: kibi/kilo, mebi/mega, gibi/giga, tebi/tera
- Number systems: binary, denary, hex, BCD; one’s & two’s complement
- Convert between number bases and representations
- Binary addition & subtraction; understand overflow
- Practical applications of BCD and hexadecimal
- Character data: ASCII, extended ASCII, Unicode
Past paper questions
Section titled “Past paper questions”(a) (i) Convert the binary number into hexadecimal. 1 mark
101100111010
(ii) Convert the denary number into Binary Coded Decimal (BCD). 1 mark
108
(iii) Convert the 12-bit two’s complement binary integer into denary. 2 marks
Show your working.
111110111100
Working
Denary value
(b) (i) The following binary addition is performed using 8-bit registers.
Complete the calculation using binary addition.
1 0 1 1 0 0 1 1 + 0 1 1 1 1 0 0 0 1 mark
(ii) Name and describe the error that can occur when binary addition is performed. 2 marks
Show mark scheme
1(a)(i) [1 mark]
B3A
1(a)(ii) [1 mark]
0001 0000 1000
1(a)(iii) [2 marks]
1 mark for the working 1 mark for the correct denary value Working: Method 1: 1111 1011 1100 Flip the bits 0000 0100 0011 Add 1 0000 0000 0001 + 0000 0100 0100 Method 2: -2048 + 1024 + 512 + 256 + 128 + 32 + 16 + 8 + 4 // -128 + 32 + 16 + 8 + 4 Denary value: -68
1(b)(i) [1 mark]
(1) 00101011
1(b)(ii) [2 marks]
1 mark per bullet point, max 2 marks • An overflow error occurs • The answer cannot be represented in the number of bits available // The answer is larger than the maximum positive number that can be stored in the register // The answer is smaller than the most negative number that can be stored in the register
(a) The following binary addition is performed using 8‑bit registers.
Complete the calculation using binary addition.
1 0 0 0 0 1 1 1 + 0 0 1 1 1 0 0 1 1 mark
(b) A computer uses the Unicode character set. 1 mark
State the number of bits used to store one character from the Unicode character set.
(c) ASCII is another character set. The ASCII value for the character ‘h’ has the denary value 104.
(i) Write the Binary Coded Decimal (BCD) value for the ASCII character ‘h’. 1 mark
(ii) Write the hexadecimal value for the ASCII character ‘h’. 1 mark
Show mark scheme
7(a) [1 mark]
1 mark for the correct answer 1100 0000
7(b) [1 mark]
1 mark for the correct answer 8 // 16 // 32 // 64
7(c)(i) [1 mark]
1 mark for the correct answer 0001 0000 0100
7(c)(ii) [1 mark]
1 mark for the correct answer 68
(a) Data in a computer system is represented in binary. 3 marks
Put one tick (3) in each row to identify the minimum number of bits used to store each example of data.
| Example of data | Number of bits | ||||||
|---|---|---|---|---|---|---|---|
| Example of data | 4 | 8 | 16 | 24 | 32 | 64 | 128 |
| the hexadecimal value F139 | |||||||
| 16 000 000 unique amplitude values | |||||||
| an IPv4 address | |||||||
| 256 unique colours | |||||||
| an IPv6 address | |||||||
| the denary value 65 000 |
(b) Convert the denary number –108 into a 12‑bit two’s complement binary number. 1 mark
(c) A three‑place arithmetic shift to the right is performed on the following two’s complement negative integer. 1 mark
Show the result of this arithmetic shift.
10010011
(d) Convert the following positive binary integer into hexadecimal. 1 mark
1110001100111011
Show mark scheme
2(a) [3 marks]
3 marks for 6 correct ticks 2 mark for 4 or 5 correct ticks 1 mark for 2 or 3 correct ticks Example of data Number of bits 4 8 16 24 32 64 128 ✓ the hexadecimal value F139 16 000 000 unique ✓ amplitude values ✓ an IPv4 address 256 unique colours ✓ ✓ an IPv6 address the denary value ✓ 65 000
2(b) [1 mark]
1 mark 1111 1001 0100
2(c) [1 mark]
1 mark 1111 0010
2(d) [1 mark]
1 mark E33B
(a) Convert the denary integer 558 into 12-bit binary and hexadecimal. 2 marks
Binary
Hexadecimal
(b) (i) Convert the two’s complement binary integer 11100010 into denary. 1 mark
(ii) Write the smallest and the largest two’s complement binary integers that can be represented in 8 bits. 2 marks
Smallest
Largest
(c) Give one application where Binary Coded Decimal (BCD) is used and justify its use. 2 marks
Application
Justification
Show mark scheme
2(a) [2 marks]
1 mark for: 0010 0010 1110 1 mark for: 22E
2(b)(i) [1 mark]
1 mark for: -30
2(b)(ii) [2 marks]
1 mark for smallest, 1 mark for largest Smallest: 1000 0000 Largest: 0111 1111
2(c) [2 marks]
1 mark for application and 1 mark for corresponding justification e.g. • an application that performs financial / banking calculations • because financial transactions use only two decimal places and must be accurate, no accumulating / rounding errors and it is difficult to represent decimal values exactly in normal binary. Or • electronic displays • because visual displays only need to show individual digits • because conversion between denary and BCD is straightforward Or • The storage of the date and time in the BIOS of a PC • because conversion between denary and BCD is more straightforward Or • Barcode systems • because conversion between denary and BCD can be accurately completed
(a) A computer can perform logical and arithmetic shifts.
(i) Show the result of a logical left shift of 2 places on the two’s complement binary integer 11001010 1 mark
(ii) Show the result of an arithmetic right shift of 3 places on the two’s complement binary integer 10011110 1 mark
(b) Complete the following binary addition. Show your working. Include any overflow bit(s).
1 1 1 1 0 1 0 1 + 1 0 1 1 0 0 0 1 1 mark
(c) Subtract the binary number 00011110 from the binary number 01100100 using binary subtraction. Show your working. 2 marks
Show mark scheme
7(a)(i) [1 mark]
1 mark for 0010 1000
7(a)(ii) [1 mark]
1 mark for 1111 0011
7(b) [1 mark]
1 mark for 1 1 1 1 0 1 0 1 + 1 0 1 1 0 0 0 1 1 1 1 1 1 (1) 1 0 1 0 0 1 1 0 Answer: (1) 1010 0110
7(c) [2 marks]
1 mark for showing binary subtraction (any method) Direct subtraction: 1 1 1 1 0 1 1 0 0 1 0 0 -0 0 0 1 1 1 1 0 1 1 1 1 0 1 0 0 0 1 1 0 Adding the two’s complement: 0 1 1 0 0 1 0 0 + 1 1 1 0 0 0 1 0 1 1 1 (1) 0 1 0 0 0 1 1 0 1 mark for answer 0100 0110
(a) State one difference between a tebibyte and a gigabyte. 1 mark
(b) (i) Convert the unsigned binary integer into hexadecimal.
110001100111
Answer [1]
(ii) Convert the two’s complement binary number into denary.
100110010111
Answer [1]
(iii) Convert the Binary Coded Decimal (BCD) into denary.
010101110011
Answer [1]
(c) Subtract the denary number 23 from the two’s complement binary number 01001010 Perform this calculation using binary subtraction. 2 marks
Show your working.
Working
Answer
Show mark scheme
1(a) [1 mark]
1 mark for: • A tebibyte = 1024 gibibytes / 1 048 576 kibibytes / 2 bytes whereas a 40 gigabyte = 1000 megabytes / 1 000 000 kilobytes / 10 bytes 9 • Tebi is binary prefix giga is denary prefix
1(b)(i) [1 mark]
1 mark for: C67
1(b)(ii) [1 mark]
1 mark for: −1641
1(b)(iii) [1 mark]
1 mark for: 573
1(c) [2 marks]
1 mark for working 1 mark for answer. Working Using the two’s complement and adding: 23 in binary = 00010111 so minus 23 is 11101001 0100 1010
- 1110 1001 (1)0011 0011 Direct subtraction: 0100 1010 – 0001 0111 0011 0011 Answer: 0011 0011
1(d) [1 mark]
1 mark from: • The answer cannot be represented in the number of bits available • The answer is larger than the maximum positive number that can be stored in the register • The answer is smaller than the most negative number that can be stored in the register
A computer system stores text, images and sound.
(a) A character set is used to represent characters in a computer. 2 marks
Identify and describe one character set.
Character set
Description
(b) The colour of each pixel in a bitmapped image is represented by 8 bits.
(i) State the largest number of different colours that can be represented by 8 bits. 1 mark
(ii) State one drawback of increasing the number of bits that represents each pixel in the bitmap image. 1 mark
(iii) A bitmap image can be compressed using lossy compression. 2 marks
Explain the reasons why lossy compression is often suitable for a bitmap image.
(c) (i) Explain how an analogue sound wave is converted into digital data. 2 marks
(ii) Describe one method of compressing a sound file using lossy compression. 2 marks
Show mark scheme
6(a) [2 marks]
1 mark for identification 1 mark for matching description e.g. • ASCII • 7/8 bits per character // represents 128/256 characters // represents all characters from Latin alphabet • UNICODE • 8/16/32 bits per character // represents 256/65536+ characters // represents all characters in all languages
6(b)(i) [1 mark]
1 mark for: 256 // 2 8
6(b)(ii) [1 mark]
1 mark for: Increased file size
6(b)(iii) [2 marks]
1 mark for each bullet point ( max 2 ) e.g. • The change may not be noticeable // Data removed is usually not noticed by the human eye • … for example, changes in shade/detail • It produces a larger decrease in file size compared to lossless // Lossy decreases file size considerably
6(c)(i) [2 marks]
1 mark for each bullet point ( max 2 ) • Value magnitude/size of the analogue sound wave is measured a set / number of times each second/time / at set intervals • Each sample/reading/measurement is given the binary number and stored in sequence
6(c)(ii) [2 marks]
1 mark for each correct point and 1 mark for matching expansion e.g. • Decrease sample rate • … fewer samples/readings/measurements stored per second // fewer bits per second stored • Decrease sample resolution • … fewer bits per sample/reading/measurement // each sample has fewer bits • Sound outside of set/human hearing range is removed • … fewer measurements are stored / decreases the number of possible binary values so fewer bits are stored
(a) Convert the hexadecimal number 1FAB into denary.
Working
Denary value [1]
(b) Explain how to convert the two’s complement integer 10011111 into denary. Give the denary value after conversion. 3 marks
Explanation
Denary value
(c) Describe the difference between a right logical binary shift and a right arithmetic binary shift. 2 marks
Show mark scheme
8(a) [1 mark]
1 mark for: Denary value: 8107
8(b) [3 marks]
1 mark for each bullet point for the method ( max 2 ) e.g. • Flip each bit then add 1 … • … method of converting the new binary number into denary • Most significant 1 bit is treated as the corresponding negative denary value … • … add the other positive corresponding denary values 1 mark for correct conversion Denary value: −97
8(c) [2 marks]
1 mark each: • A logical shift moves all bits to the right and inserts zeros in the appropriate leftmost bits • An arithmetic shift moves all bits to the right but copies the sign bit into the Most Significant Bit (MSB)
Complete the binary addition. Show your working.
1 0 0 1 1 1 1 0 0 1 1 0 0 0 0 1 + 0 0 0 1 1 0 0 1
3 marks
Show mark scheme
7 [3 marks]
1 mark each: Working – carried values clearly indicted Correct answer 0001 1000 Overflow clearly indicated as overflow Example: 1 0 0 1 1 1 1 0 0 1 1 0 0 0 0 1
- 0 0 0 1 1 0 0 1
(1) 0 0 0 1 1 0 0 0 1 1 1 1 1 1 1........................(carries)
A computer stores binary data.
(a) Tick (3) one box only to identify the largest file size. 1 mark
3300 kibibytes
0.3 megabytes
3 mebibytes
3300 kilobytes
(b) Subtract the denary number 10 from the denary number 100 using binary subtraction. 3 marks
Show your working.
Working
Answer
(c) Convert the hexadecimal number C0F into denary. 2 marks
Show your working.
Working
Answer
Show mark scheme
7(a)
1 mark for: 3300 kibibytes
7(b) [2 marks]
1 mark each: Converting 100 to binary 0110 0100 and 10 to binary 0000 1010 Subtraction method - converting 10 to – 10 and adding // direct subtraction … … correct answer 0101 1010 Method 1: Converting to -10 and adding: Binary for +10 is 0000 1010 Binary for –10 is 1111 0110 Binary for 100 is 0110 0100 100 + (-10): 0 1 1 0 0 1 0 0 +1 1 1 1 0 1 1 0 (1) 0 1 0 1 1 0 1 0 Carries: 1 1 0 0 1 0 0 0 Method 2: Direct Subtraction Borrows: 0 0 0 1 1 0 1 0 0 1 1 0 0 1 0 0 – 0 0 0 0 1 0 1 0 0 1 0 1 1 0 1 0
7(c)
1 mark for working: 1100 0000 1111 // 2048 + 1024 + 8 + 4 + 2 + 1 // (12 * 16 ) + 15 // (12 * 16
- 15 // 3072 + 15 2 1 mark for correct answer: 3087
(a) Complete the following description.
Show mark scheme
1(a) [4 marks]
1 mark for each correct answer: binary 3072 denary/decimal 2000 A kibibyte has a binary prefix. Three kibibytes is the same as 3072 bytes. A megabyte has a decimal/denary prefix. Two terabytes is the same as 2000 gigabytes.
1(b) [1 mark]
1 mark for correct answer: F1
1(c)
1 mark for a correct answer: The answer is too long to be represented in the same number of bits as the binary numbers being added
1(d)(i) [2 marks]
1 mark for all 3 answers correct: Character set Number of bits ASCII 7 extended ASCII 8 Unicode 16 / 32
1(d)(ii)
1 mark each: Each character has a unique binary code The binary code for each character is stored in sequence
(a) Draw one line from each vector graphic term to its most appropriate description. 2 marks
Term
drawing list
Description
a component created using a formula
defines one characteristic drawing object of a component
data required to create all property components in the graphic
(b) State what is meant by the bit depth of a bitmap image and explain how changing the bit depth affects the image. 3 marks
Definition
Explanation
(c) Explain why a bitmap image is often compressed before it is attached to an email. 2 marks
Show mark scheme
1(a) [2 marks]
2 marks for all 3 lines correct 1 mark for 1 line correct Description Term a component created drawing list using a formula defines one characteristic drawing object of a component data required to create all property components in the graphic
1(b) [3 marks]
1 mark for the definition • The number of bits used to represent each colour 1 mark for each bullet point for the explanation • Increase in bit depth means the image has a greater range of colours // Decrease in bit depth means the image has a smaller range of colours • Increase in bit depth makes the image closer to the original / more realistic // Decrease in bit depth makes the image less like the original / less realistic
1(c) [2 marks]
1 mark for each bullet point ( max 2 ) • Reduced bandwidth usage when transmitting the message • Reduced transmission time from email client to email server • Reduced storage space on the email • Email accounts often have a maximum size for an attachment
(a) State one difference between a kibibyte and a megabyte. 1 mark
(b) (i) Convert the denary value into a 12-bit two’s complement binary integer.
−196 Answer [1]
(ii) Convert the Binary Coded Decimal (BCD) into denary.
100001100101
Answer [1]
(iii) Convert the unsigned binary integer into denary.
000111010110
Answer [1]
(c) Identify one practical application of BCD and justify why BCD is used in this application. 2 marks
Application
Justification
Show mark scheme
3(a) [1 mark]
1 mark for: Either • 10 kibibyte = 1,024 bytes // 2 bytes and 3 6 megabyte = 1000 kilobytes //1 000 000 bytes // 10 kilobytes // 10 bytes Or • kibi is binary prefix and mega is denary prefix
3(b)(i) [1 mark]
1111 0011 1100
3(b)(ii) [1 mark]
865
3(b)(iii) [1 mark]
470
3(c) [2 marks]
1 mark for a correct application 1 mark for a corresponding justification • An application that performs financial / banking calculations • ... because it is difficult to represent decimal values exactly in normal binary and financial transactions use only two decimal places and must be accurate, no accumulating errors Or • Electronic displays, e.g. calculators, digital clocks • ... because visual displays only need to show individual digits • ... because conversion between denary and BCD is easier Or • The storage of the date and time in the BIOS of a PC • ... because conversion with denary is easier
(a) Describe the impact of increasing the image resolution on the quality of a bitmap graphic. 2 marks
(b) Calculate the file size of a bitmap image using the following information: 2 marks
image resolution of 2048 pixels wide and 1024 pixels high
bit depth of 16 bits.
Give your answer in kibibytes. Show your working.
Working
Answer in kibibytes
Show mark scheme
2(a) [2 marks]
1 mark for each bullet point: • more pixels can be stored / are available • the image is sharper / less pixelated
2(b) [2 marks]
1 mark for answer. 1 mark for working Answer: 4096 kibibytes Working: File size = (2048 1024 16) / (8 1024)
A computer has an Operating System (OS).
(a) Describe how the Operating System manages the peripheral hardware devices of the computer. 4 marks
(b) Hardware management is one key management task carried out by the Operating System. 2 marks
Identify two other key management tasks carried out by the Operating System.
1
2
(c) The Operating System has utility software including defragmentation software. 3 marks
Explain how defragmentation can improve the performance of the computer.
(d) The computer stores data in binary form.
(i) State the difference between a kibibyte and a kilobyte. 1 mark
(ii) Convert the denary number 964 into Binary Coded Decimal (BCD). 1 mark
(iii) Convert the positive binary integer 11110010 into hexadecimal. 1 mark
(iv) Give the smallest and largest two’s complement binary number that can be represented using 8 bits. 2 marks
Smallest
Largest
(v) Add the following two binary integers using binary addition. Show your working. 2 marks
1 0 1 1 0 0 0 0 + 0 0 0 1 1 0 1 1
(vi) Show the result of a 3‑place right logical shift on the binary number: 1 mark
11001100
Show mark scheme
3(a) [4 marks]
1 mark each to max 4 Examples: Installs device drivers … to allow communication between peripherals and computer Sends data and receives data to and from peripherals … such as to an output device and from an input device/by example Handles buffers for transfer of data … to ensure smooth transfer between devices that transmit and receive at different speeds Manages interrupts / signals from the device
3(b) [2 marks]
1 mark each to max 2 Memory management File management Security management Process management Error checking and recovery
3(c) [1 mark]
1 mark each to max 3 Rearranges blocks of individual files (on the HDD) so they are contiguous // moves the free space together Accessing each file is faster …because there is no need to search for the next fragment / block of the file …so less head movement is needed
3(d)(i)
1 mark from Kibibyte is 1024 bytes and kilobyte is 1000 bytes Kibibyte is binary prefix and kilobyte is denary prefix
3(d)(ii) [1 mark]
1001 0110 0100
3(d)(iii) [1 mark]
F2
3(d)(iv) [2 marks]
Smallest: 10000000 Largest: 01111111
3(d)(v)
1 mark for working 1 mark for answer 1 0 1 1 0 0 0 0
- 0 0 0 1 1 0 1 1 1 1 0 0 1 0 1 1 1 1
3(d)(vi) [2 marks]
00011001
Data in a computer is stored in binary form.
(a) State the number of unique binary values that can be represented in 16 bits. 1 mark
(b) Give the 8‑bit one’s complement representation of the denary number −120. 2 marks
Show your working.
Working
Answer
(c) Convert the hexadecimal number A04 into denary. 2 marks
Show your working.
Working
Answer
(d) Show the result of a 2‑place left logical shift on the binary number: 1 mark
01001111
Show mark scheme
4(a) [2 marks]
2 // 65536 16
4(b)
1 mark for working; 1 mark for answer Working: +120 = 0111 1000 Answer: 1000 0111
4(c) [2 marks]
1 mark for working; 1 mark for answer ) + 4 Working: A04 = (10 * 16 2 // A04 = (10 * 256) + 4 // A04 = 1010 0000 0100 Answer: 2564
4(d) [1 mark]
0011 1100
A computer stores data in binary form.
(a) Draw one line from each description to its matching denary value.
Description Denary value
- 127
The smallest integer that can be represented in 8-bit two’s complement.
The largest integer that can be represented in 8-bit two’s complement.
The largest unsigned integer that can be represented in 8 bits.
(b) The computer has a Control Unit (CU), system clock and control bus. 3 marks 4 marks 2 marks
127
255
128
256
256
128
255 Explain how the CU, system clock and control bus operate to transfer data between the components of the computer system.
| Complete the table by writing the regist Fetch-Execute (F-E) cycle given in the table. | ter transfer notation for each stage of the |
|---|---|
| Stage description | Register transfer notation |
| The Program Counter (PC) is incremented | ______ |
| The data in the address stored in the Memory Address Register (MAR) is copied to the Memory Data Register (MDR) |
______ |
Show mark scheme
7(a) [4 marks]
1 mark for each correct line Description Denary value The smallest integer that can 127 be represented in 8-bit two's complement. 127 255 128 The largest integer that can be represented in 8-bit two's 256 complement. 256 128 The largest unsigned integer that can be represented in 8 255 bits.
7(b)
1 mark each to max 4 The system clock gives out timing signals … which are sent on the control bus …to synchronise the other system components The Control Unit initiates data transfer …by generating signals that are sent on the control bus to other components
7(c) [2 marks]
1 mark for each Register transfer notation Stage description Register transfer notation The Program Counter (PC) is PC [PC] + 1 incremented The data in the address stored in the MDR [[MAR]] Memory Address Register (MAR) is copied to the Memory Data Register (MDR)
Draw one line from each security feature to its most appropriate description.
Security feature Description
converts data to an alternative form
firewall
redirects a user to a fake website
pharming
verifies the authenticity of data
anti-virus software
scans files on the hard drive for malicious software
encryption
accepts or rejects incoming and outgoing packets based on criteria 4 marks
Show mark scheme
2 [4 marks]
1 mark for each correct line. Description Security feature converts data to an alternative form firewall redirects a user to a false website pharming verifies the authenticity of data anti-virus software scans files on the hard drive for malicious software encryption accepts or rejects incoming and outgoing packets based on criteria
(a) Draw one line from each utility software to its most appropriate purpose. 5 marks
Utility software
Purpose
virus checker
disk formatter
backup
disk repair
defragmentation
to reorganise files so they are contiguous
to scan for malicious program code
to decrease the file size
to initialise a disk
to create copies of files in case the original is lost
to check for and fix inconsistencies on a disk
(b) Compilers and interpreters translate programs written in a high-level language into a low-level language.
(i) State two drawbacks of using a compiler compared to an interpreter during program development. 2 marks
1
2
(ii) Explain why high-level language programs might be partially compiled and partially interpreted. 2 marks
Show mark scheme
1(a) [5 marks]
1 mark for each correct line. Utility software Purpose to reorganise files so virus checker they are contiguous to scan for malicious program code disk formatter to decrease the file size backup to initialise a disk to create copies of files disk repair in case the original is lost to check for and fix defragmentation inconsistencies on a disk
1(b)(i) [2 marks]
1 mark for each bullet point (max 2) : • larger amounts of source code take time to compile • slower to produce the object code than an interpreter • code cannot be changed without recompilation • the program will not run if there are any errors • errors cannot be corrected in real-time • one error may result in other false errors being reported • cannot easily test specific sections of the source code // cannot easily test unfinished source code
1(b)(ii) [2 marks]
1 mark for each bullet point (max 2) : • partially compiled programs can be used on different platforms as they are interpreted when run • code is optimised for the CPU as machine code is generated at run time
A digital audio message needs to be recorded.
| Tick () one box in each row to identify recording. | y the effect of ea | ach action on th | he accuracy of the |
|---|---|---|---|
| Action | Accuracy increases |
Accuracy decreases |
Accuracy does not change |
| Change the sampling rate from 40 kHz to 60 kHz. |
|||
| Change the duration of the recording from 20 minutes to 40 minutes. |
|||
| Change the sampling resolution from 24 bits to 16 bits. |
|||
| 2 marks |
(b) The audio message is recorded with a sampling rate of 50 kHz and a sampling resolution of 16 bits. 2 marks
The recording is 20 minutes in length.
Calculate the file size of the recording.
Give your answer in megabytes and show your working.
Working
Answer ______ megabytes
(c) A computer uses a buffer when playing the audio message. 3 marks
Explain the purpose of a buffer in a computer system using one other example.
Show mark scheme
1(a) [2 marks]
1 mark for one or two correct ticks, 2 marks for three correct ticks. Accuracy Accuracy Accuracy Action increases decreases does not change Change the sampling rate from ✓ 40 kHz to 60 kHz. Change the duration of the ✓ recording from 20 minutes to 40 minutes. Change the sampling resolution ✓ from 24 bits to 16 bits.
1(b) [2 marks]
1 mark for answer; 1 mark for working. Working: Size = 50KHz * (20 60) * 16 bits = 50 000 * 1200 * 16 bits // 50 000 *1200 * 2 bytes = 960 000 000 bits = 120 000 000 bytes = 120 000 kilobytes = 120 megabytes Answer = 120 megabytes
1(c) [3 marks]
1 mark for purpose ( max 2 ): Purpose: • to act as temporary storage // to store (downloaded) data • ... before it is used by the receiving device • ... to allow processes / devices to operate at different speeds // independently of each other 1 mark for each example ( max 1 ): Examples: • printer buffer used when data is transferred from a computer to a printer • video buffer when streaming videos • keyboard buffer when performing data entry
Computers store data in binary form.
(a) State the difference between a tebibyte and a terabyte. 1 mark
(b) Convert the signed denary value –100 into an 8-bit two’s complement binary integer.
Working
Answer [1]
(c) Convert the denary number 251 into hexadecimal. Show your working. 2 marks
Working
Answer
(d) Add the following unsigned binary integers. 1 mark
0 1 0 1 0 0 0 0 + 0 0 1 1 1 1 1 0
Show mark scheme
1(a)
1 mark for: one tebibyte is 1024 gibibytes and one terabyte is 1000 gigabytes
1(b) [2 marks]
1001 1100
1(c)
1 mark for working e.g. Dividing by 16 // converting to binary (11111011) 1 mark for answer FB
1(d) [5 marks]
1000 1110
Text and numbers are examples of data stored in a computer.
(a) A character set is used to represent characters in a computer.
(i) Describe what is meant by a character set . 2 marks
(ii) Identify two character sets and state one difference between them. 3 marks
Character set 1
Character set 2
Difference
(iii) Describe how lossless compression can be used to reduce the file size of a text file. 2 marks
(iv) Explain why lossy compression should not be used on a text file. 2 marks
Show mark scheme
1(a)(i)
1 mark per point to max 2 All of the characters/symbols that the computer can use/represent Each character has a unique number/binary number/hexadecimal number
1(a)(ii) [3 marks]
1 mark for each character set to max 2 , 1 mark for difference ASCII Extended ASCII UNICODE ASCII has 7 bits whereas UNICODE has 16 bits Extended ASCII has 8 bits whereas UNICODE has 16 bits ASCII has 7 bits whereas extended ASCII has 8 bits Unicode can represent more characters than ASCII/Extended// by example Extended ASCII can represent more characters than ASCII
1(a)(iii) [2 marks]
1 mark per point to max 2 Can use run-length encoding Identifies groups of repeated characters ... ... replaces them with a one copy of the character and the number of times it occurs
1(a)(iv) [2 marks]
1 mark per point to max 2 None of the original data can be lost / deleted The (text) file would be corrupted // the (text) file cannot be opened
1(b) [5 marks]
1 mark for each correct value Statement The hexadecimal value 11 represented in denary 17 The smallest denary number that be represented by an 0 unsigned 8-bit binary integer The denary number 87 represented in Binary Coded 1000 0111 Decimal (BCD) The denary number 240 represented in hexadecimal F0 The denary number –20 represented in 8-bit two’s 1110 1100 complement binary
(a) Draw one line from each binary value to its equivalent (same) value on the right. 5 marks
Binary value
8 bits
8000 bits
1000 kilobytes
1024 mebibytes
8192 bits
(b) (i) Perform the following binary addition. Show your working. 2 marks
10101010 + 00110111
(ii) State how an overflow can occur when adding two binary integers. 1 mark
1 kibibyte
1 gigabyte
1 byte
1 kilobyte
1 gibibyte
1 megabyte
1 mebibyte
(c) Convert the hexadecimal value F0 into denary. 1 mark
Show mark scheme
1(a)
1 mark for each correct line 1 kibibyte 8 bits 1 gigabyte 8000 bits 1 byte 1000 kilobytes 1 kilobyte 1024 mebibytes 1 gibibyte 8192 bits 1 megabyte 1 mebibyte
1(b)(i) [2 marks]
1 mark for answer 1 mark for working e.g. 1010 1010 0011 0111 1110 0001 1 1 1 1 1 1
1(b)(ii) [1 mark]
The result is a larger number than can be stored in the given number of bits. // The result is greater than 255
1(c) [1 mark]
240
A register stores the following binary number:
1 1 0 0 1 1 0 1
(a) The binary value in the register represents an unsigned binary integer. 1 mark
Convert the unsigned binary integer into denary.
(b) The binary value in the register represents a two’s complement binary integer. 1 mark
Convert the two’s complement binary integer into denary.
(c) The binary value in the register represents a hexadecimal number. 1 mark
Convert the binary number into hexadecimal.
(d) State why the value in the register cannot be interpreted as a Binary Coded Decimal (BCD). 1 mark
| f two re | egister | rs are: | |||||
|---|---|---|---|---|---|---|---|
0 |
0 |
1 |
1 |
1 |
1 |
0 |
1 |
0 |
0 |
1 |
0 |
1 |
1 |
0 |
1 |
(i) Add the contents of Register 1 and Register 2 . Show your working. 2 marks
Answer
Show mark scheme
4(a) [1 mark]
205
4(b) [1 mark]
– 51
4(c) [1 mark]
4(d) [2 marks]
1 mark for: The denary value in each group of 4 bits is greater than 9 // the denary value in each nibble is greater than 9
4(e)(i) [2 marks]
1 mark for working, 1 mark for answer 0011 1101 +0010 1101 0110 1010 111 1 1
4(e)(ii)
1 mark for working, 1 mark for answer 0011 1101 (two’s complement) +1101 0011 0001 0000 1111 111
(a) Draw one line from each binary value to its equivalent (same) value on the right. 5 marks
Binary value
8 bits
8000 bits
1000 kilobytes
1024 mebibytes
8192 bits
(b) (i) Perform the following binary addition. Show your working. 2 marks
10101010 + 00110111
(ii) State how an overflow can occur when adding two binary integers. 1 mark
1 kibibyte
1 gigabyte
1 byte
1 kilobyte
1 gibibyte
1 megabyte
1 mebibyte
(c) Convert the hexadecimal value F0 into denary. 1 mark
Show mark scheme
1(a)
1 mark for each correct line 1 kibibyte 8 bits 1 gigabyte 8000 bits 1 byte 1000 kilobytes 1 kilobyte 1024 mebibytes 1 gibibyte 8192 bits 1 megabyte 1 mebibyte
1(b)(i) [2 marks]
1 mark for answer 1 mark for working e.g. 1010 1010 0011 0111 1110 0001 1 1 1 1 1 1
1(b)(ii) [1 mark]
The result is a larger number than can be stored in the given number of bits. // The result is greater than 255
1(c) [1 mark]
240
A computer uses the ASCII character set.
(a) State the number of characters that can be represented by the ASCII character set and the extended ASCII character set. 2 marks
ASCII
Extended ASCII
(b) Explain how a word such as ‘HOUSE’ is represented by the ASCII character set. 2 marks
(c) Unicode is a different character set.
The Unicode value for the character ‘1’ is denary value 49.
(i) Write the hexadecimal value for the Unicode character ‘1’. 1 mark
(ii) Write the denary value for the Unicode character ‘5’. 1 mark
Show mark scheme
6(a) [2 marks]
1 mark for each correct answer ASCII = 128 // 2 7 Extended ASCII = 256 // 2 8
6(b) [2 marks]
1 mark per bullet point to max 2 Each character has its own unique code • Each character in the word is replaced by its code • The codes are stored in the order in the word •
6(c)(i) [1 mark]
31
6(c)(ii) [1 mark]
53