Data Representation (Cambridge (CIE) A Level Computer Science): Exam Questions

A computer system stores text, images and sound.

A character set is used to represent characters in a computer.

Identify and describe one character set.

Character set ....................

Description .......................

Convert the hexadecimal number 1FAB into denary.

Working ............................

Denary value .....................

Explain how to convert the two’s complement integer 10011111 into denary.

Give the denary value after conversion.

Explanation ......................

Denary value .....................

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

A computer stores binary data.

Tick (✓) one box only to identify the largest file size.

☐ 3300 kibibytes

☐ 0.3 megabytes

☐ 3 mebibytes

☐ 3300 kilobytes

Subtract the denary number 10 from the denary number 100 using binary subtraction.

Show your working.

Convert the hexadecimal number C0F into denary.

Show your working

Complete the following description.

A kibibyte has a ................................................ prefix. Three kibibytes is the same as ................................................ bytes.

A megabyte has a ................................................ prefix. Two terabytes is the same as ................................................ gigabytes.

Convert the denary number 241 to hexadecimal

State what is meant by an overflow in binary addition.

Computers use character sets when representing characters in binary.

(i) Complete the table by identifying the number of bits each of the character sets allocates to each character.

(1)

(ii) Explain how the word ‘Clock’ is represented by a character set.

(2)

State one difference between a kibibyte and a megabyte.

(i) Convert the denary value into a 12-bit two’s complement binary integer.

−196

(1)

(ii) Convert the Binary Coded Decimal (BCD) into denary.

100001100101

(1)

(iii) Convert the unsigned binary integer into denary.

000111010110

(1)

Identify one practical application of BCD and justify why BCD is used in this application.

Complete the table by giving the value of each binary prefix as a power of 2 and as a number of bytes.

A photograph is stored as a file of 3 145 728 bytes.

Calculate the size of this file in mebibytes (MiB).

Show your working.

A hard disk drive is advertised by its manufacturer as having a capacity of 500 GB.

When the drive is connected, the operating system reports its capacity as approximately 466 GiB.

Explain why the two figures are different, and show how the value of 466 GiB is obtained.

Complete the table by converting each value into the number system shown.

Binary Coded Decimal (BCD) is one way of representing denary numbers in a computer system.

State two devices or systems that use BCD to represent numbers.

ASCII is a character set.

(a) State the number of bits ASCII uses to represent one character.

(b) State the maximum number of different characters ASCII can represent.

A temperature sensor produces the denary reading 173.

Convert 173 into:

• an 8-bit unsigned binary integer

• a hexadecimal value

Show your working.

A bank uses a computer system to store the balance of each customer account.

The system stores every balance in Binary Coded Decimal (BCD) rather than in pure binary.

Explain why BCD is used for this application.

The table shows part of an ASCII code table. Each character is shown with its ASCII code in denary and as a 7-bit binary number.

Complete the three empty cells in the table.

A student is asked to convert the unsigned binary integer 1011011110 into hexadecimal.

The student groups the bits into fours starting from the left, adds two zeros on the right to fill the last group, and writes the answer as B78.

Show that the student's answer is wrong, and give the correct hexadecimal value.

A shop uses a digital weighing scale. The scale has a display that shows the mass as four separate denary digits.

The control system inside the scale stores the mass in Binary Coded Decimal (BCD).

Explain why BCD is used in this application, and give one disadvantage of using BCD instead of pure binary.

(a) Convert the denary number 507 into Binary Coded Decimal (BCD).

(b) Convert the BCD value 1000 0010 0110 into denary.

A computer stores each character a user types as a 7-bit ASCII code.

The table shows three ASCII codes in denary.

(a) The user types the character 'e'. Show how the 7-bit ASCII code for 'e' is worked out and write the code in binary.

(b) A program converts the character 'e' to the character 'E'. Show how the ASCII code for 'E' is worked out from the ASCII code for 'e' and write the code in binary.

Complete the binary addition of the two 8-bit unsigned binary integers.

  00101101

+ 01010110

Show your working.

Hexadecimal is used in a computer system when a value has to be shown to a person.

Complete the table by identifying what each hexadecimal value represents.

A 16-bit register holds the following bit pattern.

0111 0011 0000 1001

(a) The bit pattern is a Binary Coded Decimal (BCD) value. Give the denary value it represents.

(b) The same 16 bits are then read as an unsigned binary integer. Calculate the denary value in this case.

Show your working.

ASCII uses 7 bits to represent each character. Extended ASCII uses 8 bits.

Calculate how many more characters extended ASCII can represent than ASCII.

Show your working.

A computer stores integers as 8-bit two's complement binary numbers.

Calculate the sum of 01101001 and 10110100.

Show your working.

Give the answer as an 8-bit two's complement binary number and as a denary number.

A network technician needs to write down the MAC address of a device.

A MAC address is 48 bits long. It is written as 12 hexadecimal digits.

Explain why a MAC address is written in hexadecimal rather than in binary.

A text editor is changed so that it stores characters using extended ASCII instead of ASCII.

Describe the effect of this change on the characters the text editor can store.

A 12-bit register holds the bit pattern 0110 1011 0010.

A student says that this is a Binary Coded Decimal (BCD) value.

(a) Explain why the student is wrong.

(b) State the largest denary value that this 12-bit register can hold using BCD, and the largest denary value it can hold using unsigned binary.

A processor stores integers as 8-bit two's complement binary numbers.

It adds three values in order. It adds B to A, then adds C to that result.

A = 01011010

B = 11100111

C = 10111101

Show your working for both additions.

Give the result of each addition as an 8-bit two's complement binary number and as a denary number.

An IPv4 address is 32 bits long. It is written as four denary numbers separated by full stops.

An IPv6 address is 128 bits long. It is written as eight groups separated by colons, and each group is written in hexadecimal.

Explain why hexadecimal is used to write an IPv6 address.

Give the 8-bit representation of the denary value -37 in:

(a) one's complement

(b) two's complement

A school stores the names of its students using extended ASCII. Some of the names contain accented letters.

(a) Explain why ASCII could not store these names but extended ASCII can.

(b) The school opens a second site in Japan and needs to store the students' names in Japanese.

Explain why extended ASCII cannot store these names.

A computer adds two binary integers and stores the result in a register.

Describe what is meant by an overflow.

An 8-bit register holds the bit pattern 10110110.

(a) The bit pattern is a two's complement binary integer. Convert it into denary.

Show your working.

(b) The same bit pattern is then read as a one's complement binary integer. Give the denary value in this case.

Unicode is a character set.

(a) State one number of bits Unicode can use to represent one character.

(b) State the number of different characters that can be represented using the number of bits you gave in part (a).

A register stores unsigned binary integers in 8 bits.

The two values 11001010 and 01101001 are added.

Explain why this addition causes an overflow.

Show your working.

A document contains 4 000 characters. Each character is stored using 16-bit Unicode.

Calculate the size of the document in bytes.

Show your working.

An 8-bit register uses two's complement to store signed integers.

(a) State the range of denary values that the register can hold.

(b) Explain why this range contains one more negative value than positive value.

(c) State the range of denary values the register could hold if it used one's complement instead, and give the reason for the difference.

A computer stores integers as 8-bit two's complement binary numbers.

Two additions are performed.

Addition P

  01011001

+ 00110100

Addition Q

  11010011

+ 10110101

Explain which of these two additions causes an overflow.

Show the result of each addition in your answer.

A messaging application stores every message using 8-bit extended ASCII. The company that owns the application wants its users to be able to send messages in Greek, Arabic, Hindi and Japanese.

The company decides to store messages using 16-bit Unicode instead.

Explain the benefits and the drawbacks of this change.

A computer stores integers as 8-bit two's complement binary numbers.

It performs the subtraction 01010110 - 00010011 by adding the two's complement of 00010011.

Show your working and give the answer as an 8-bit binary number.

A computer stores integers as 8-bit two's complement binary numbers.

Calculate 00101100 - 01111010 using binary subtraction.

Show your working.

Give the answer as an 8-bit two's complement binary number and as a denary number.

A computer stores integers as 8-bit two's complement binary numbers.

It calculates A - B - C for these three values.

A = 01100100

B = 00011110

C = 01001011

The processor performs each subtraction by adding a two's complement.

Calculate the result of A - B - C.

Show your working for both steps and give the final answer as an 8-bit two's complement binary number and as a denary number.