Cambridge International AS & A Level

* 6 1 9 5 6 0 3 6 9 4 *

COMPUTER SCIENCE 9608/31

Paper 3 Advanced Theory May/June 2021

1 hour 30 minutes

You must answer on the question paper.

No additional materials are needed.

INSTRUCTIONS
● Answer all questions.
● Use a black or dark blue pen.
● Write your name, centre number and candidate number in the boxes at the top of the page.
● Write your answer to each question in the space provided.
● Do not use an erasable pen or correction fluid.
● Do not write on any bar codes.
● You may use an HB pencil for any diagrams, graphs or rough working.
● Calculators must not be used in this paper.

INFORMATION
● The total mark for this paper is 75.
● The number of marks for each question or part question is shown in brackets [ ].
● No marks will be awarded for using brand names of software packages or hardware.

This document has 16 pages. Any blank pages are indicated.

DC (LO) 214518
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1 In a particular computer system, two real numbers, A and B, are stored using floating-point
representation with:

• 12 bits for the mantissa

• 4 bits for the exponent
• two’s complement form for both mantissa and exponent.

Number A Mantissa Exponent

1 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0

Number B Mantissa Exponent

0 1 1 1 0 0 0 0 0 0 0 0 1 1 1 1

(a) (i) Identify whether each number is positive or negative. Justify your answer.

Number A .........................................................................................................................

...........................................................................................................................................

Number B .........................................................................................................................

...........................................................................................................................................
[2]

(ii) Convert the binary values of the mantissa and the exponent for each number to their
separate denary values.

A mantissa ........................................................................................................................

...........................................................................................................................................

A exponent ........................................................................................................................

...........................................................................................................................................

B mantissa ........................................................................................................................

...........................................................................................................................................

B exponent ........................................................................................................................

...........................................................................................................................................
[4]

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(iii) Calculate the denary value of each floating-point number using your values from
part (a)(ii).

Number A .........................................................................................................................

...........................................................................................................................................

...........................................................................................................................................

Number B .........................................................................................................................

...........................................................................................................................................

...........................................................................................................................................
[2]

(b) State which number, A or B, is stored in normalised floating-point form. Justify your answer.

Number .....................................................................................................................................

Justification ...............................................................................................................................

...................................................................................................................................................

...................................................................................................................................................

...................................................................................................................................................

...................................................................................................................................................
[3]

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2 The TCP/IP protocol suite can be viewed as a stack with four layers.

(a) Write the correct descriptions for the two layers and the correct layers for the two descriptions
given in the following table.

Layer Description

Application

Handles forwarding of packets

Internet /
Network

Handles how data is physically sent

[4]

(b) (i) Explain why communication protocols are necessary.

...........................................................................................................................................

...........................................................................................................................................

...........................................................................................................................................

..................................................................................................................................... [2]

(ii) Identify and describe one other communication protocol. State its purpose.

Protocol .............................................................................................................................

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

...........................................................................................................................................

Purpose .............................................................................................................................

...........................................................................................................................................
[3]

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3 Describe, with the aid of a diagram for each one, the bus and star network topologies.

Bus

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

..........................................................................................................................................................

..........................................................................................................................................................

..........................................................................................................................................................

..........................................................................................................................................................

..........................................................................................................................................................

Star

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

..........................................................................................................................................................

..........................................................................................................................................................

..........................................................................................................................................................

..........................................................................................................................................................

..........................................................................................................................................................
[6]

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4 (a) The truth table for a logic circuit with four inputs is shown.

INPUT OUTPUT
P Q R S X
0 0 0 0 1

0 0 0 1 0

0 0 1 0 1

0 0 1 1 0

0 1 0 0 0

0 1 0 1 0

0 1 1 0 0

0 1 1 1 0

1 0 0 0 0

1 0 0 1 0

1 0 1 0 0

1 0 1 1 0

1 1 0 0 0

1 1 0 1 1

1 1 1 0 0

1 1 1 1 1

(i) Write the Boolean expression for the truth table as a sum-of-products.

X = .............................................................................................................................. [2]

(ii) Complete the Karnaugh Map (K-map) for the truth table.

PQ
00 01 11 10
00
01
RS
11
10
[2]

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(iii) The K-map can be used to simplify the expression in part (a)(i).

Draw loops around appropriate groups of 1s in the table in part (a)(ii) to produce an
optimal sum-of-products. [2]

(iv) Write the simplified sum-of-products expression for your answer to part (a)(iii).

X = ............................................................................................................................... [2]

(b) Simplify your expression for X in part (a)(i) using Boolean algebra. Show your working.

...................................................................................................................................................

...................................................................................................................................................

............................................................................................................................................. [2]

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5 The following syntax diagrams for a programming language show the syntax of:

• an assignment statement
• a variable
• an unsigned integer
• a digit
• a letter
• an operator

assignment statement

variable = variable operator variable

unsigned
integer

variable

letter letter

unsigned integer

digit digit

letter operator digit

X + 1

Y – 2

Z * 3

(a) Give reasons why each of these statements is invalid.

X = XY + 21

...................................................................................................................................................

YZ := YZ * 3

...................................................................................................................................................

XY = XY − 5

...................................................................................................................................................
[3]

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(b) Complete the Backus-Naur Form (BNF) for the syntax diagrams shown.

<letter> has been completed for you.

<letter> ::= X|Y|Z

<assignment_statement> ::=

...................................................................................................................................................

<variable> ::=

...................................................................................................................................................

<digit> ::=

...................................................................................................................................................

<unsigned_integer> ::=

...................................................................................................................................................

<operator> ::=

...................................................................................................................................................
[5]

(c) The syntax of a variable is changed to allow one or two letters followed by zero, one or two
digits.

(i) Draw an updated syntax diagram for the variable.

[3]

(ii) Give the BNF for the revised variable.

...........................................................................................................................................

...........................................................................................................................................

...........................................................................................................................................

...........................................................................................................................................

..................................................................................................................................... [3]

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6 Encryption is used to provide security when messages are transferred over a communication link.

(a) (i) Explain the way in which asymmetric key cryptography is used to encrypt a message
being sent from one computer user to another over the Internet.

...........................................................................................................................................

...........................................................................................................................................

...........................................................................................................................................

...........................................................................................................................................

...........................................................................................................................................

...........................................................................................................................................

...........................................................................................................................................

.................................................................................................................................... [4]

(ii) State two benefits of using asymmetric key cryptography.

1 ........................................................................................................................................

...........................................................................................................................................

2 ........................................................................................................................................

...........................................................................................................................................
[2]

(b) (i) Explain the way in which Transport Layer Security (TLS) provides communication
security over a computer network.

...........................................................................................................................................

...........................................................................................................................................

...........................................................................................................................................

...........................................................................................................................................

...........................................................................................................................................

...........................................................................................................................................

...........................................................................................................................................

..................................................................................................................................... [4]

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(ii) State two situations where the use of TLS would be appropriate.

1 ........................................................................................................................................

...........................................................................................................................................

2 ........................................................................................................................................

...........................................................................................................................................
[2]

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7 Four shipping containers are used to store goods on the dockside at a port. The temperature
inside each container should be kept between 5 and 8 degrees Celsius inclusive.
Each container has a temperature sensor.

A computer system is programmed to control each container’s temperature by:

• turning on the heater and turning off the air conditioning unit when the temperature falls below
5 degrees
• turning off the heater and turning on the air conditioning unit when the temperature rises
above 8 degrees.

(a) (i) State the name given to the type of system described.

..................................................................................................................................... [1]

(ii) Justify your answer to part (i).

...........................................................................................................................................

...........................................................................................................................................

...........................................................................................................................................

..................................................................................................................................... [2]

(b) The computer system stores the temperature readings for the four sensors in two’s
complement form and in four eight-bit memory locations with addresses 301 to 304.

301 0 0 0 0 1 0 0 1 Container 1

302 0 0 0 0 0 1 1 1 Container 2

303 0 0 0 0 0 1 1 0 Container 3

304 1 1 1 1 1 1 1 0 Container 4

State the container number(s) where the temperature is out of range and give the value(s) of
these temperature(s) in denary.

...................................................................................................................................................

...................................................................................................................................................

...................................................................................................................................................

............................................................................................................................................. [2]

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(c) The status of the heaters and the air conditioning units is shown at location 300.

A value of 1 means that the device is on and a value of 0 (zero) means that the device is off.

The status of the heaters is shown in the most significant four bits; the status of the air
conditioning units is shown in the least significant four bits.

The pattern of bits at location 300 shows that the heater for container 4 is on and the air
conditioning unit for container 1 is on.

Container number

1 2 3 4 1 2 3 4
300 0 0 0 1 1 0 0 0
Heater Air conditioning

Show the pattern of bits when the heater is on for containers 1 and 2 and no air conditioning
units are on.

300

[1]

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(d) The following table shows assembly language instructions for the container computer system
that has one general purpose register, the Accumulator (ACC).

Instruction
Explanation
Label Op code Operand
LDM &n Load the hexadecimal number n to ACC
Load the contents of the location at the given
LDD <address>
address to ACC
Store the contents of ACC at the given
STO <address>
address
Bitwise AND operation of the contents of ACC
AND &n
with the hexadecimal number n
Bits in ACC are shifted denary number n
LSL #n places to the left. Zeros are introduced at the
right hand end
Compare the contents of ACC with the
CMP &n
hexadecimal number n
Following a compare instruction, jump to
JPE <address>
<address> or <label> if the compare was True
<label>: <op code> <operand> Labels an instruction

If the bit for a container’s heater and the bit for the same container’s air conditioning unit are
both set to 1, a routine at label ERROR is executed. This routine has not been provided.

(i) These assembly language instructions check for an error in the container 1 system.

LDD 300
AND &88
CMP &88
JPE ERROR

Explain the purpose of each instruction.

...........................................................................................................................................

...........................................................................................................................................

...........................................................................................................................................

...........................................................................................................................................

...........................................................................................................................................

...........................................................................................................................................

...........................................................................................................................................

..................................................................................................................................... [4]

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(ii) Write the assembly language instructions to check for an error in the container 4 system.

...........................................................................................................................................

...........................................................................................................................................

...........................................................................................................................................

...........................................................................................................................................

...........................................................................................................................................

..................................................................................................................................... [3]

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© UCLES 2021 9608/31/M/J/21