AQA A-Level Computer Science AS Paper 2, June 2025: Question 2
11 marks · Medium difficulty · Calculation
Perform various binary representation tasks including calculating total byte values, binary-to-decimal conversion, unsigned binary addition, two's complement range, two's complement subtraction, and unsigned fixed-point representation.
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Question text
02.1 How many different values can be represented using one byte?
[1 mark]
02.2 The bit pattern in Figure 1 represents an 8-bit unsigned binary integer.
Figure 1
01 0 0 0 0 1 1
Convert the bit pattern in Figure 1 to decimal.
[1 mark]
02.3 Show how the 8-bit unsigned binary number 01001111 can be added to the 8-bit
unsigned binary number 00001011 without converting the numbers into decimal.
You must show all your working in binary.
[2 marks]
01 0 0 1 1 1 1
+ 0 0 0 0 1 0 1 1
… 4
02.4 What are the lowest and highest values that can be represented by a
4-bit two’s complement binary integer?
Give your answers in decimal.
[2 marks]
Lowest
Highest
02.5 Using 8-bit two’s complement binary, what is the result of subtracting 00110100
from 01101101?
Give your answer in 8-bit two’s complement binary.
You must show all your working in binary.
[3 marks]
02.6 Represent 5.75 as an 8-bit unsigned fixed point binary number with four bits before
and four bits after the binary point.
[2 marks]
Mark scheme
Show the mark scheme
Qu Pt Marking Guidance Marks
02 1 Mark is for AO2 (application) 1
256 // 28;
Qu Pt Marking Guidance Marks
02 2 Mark is for AO2 (application) 1
67;
Qu Pt Marking Guidance Marks
02 3 Marks are for AO2 (application) 2
Answer: 0101 1010;
Carry row: 000 1111;
The 1 carry bits (or some similar notation) must be shown in the correct sequence
but 0 carry bits can be omitted and the columns may be shifted.
Some working must be shown for any marks to be awarded.
Qu Pt Marking Guidance Marks
02 4 Marks are for AO2 (application) 2
–8 (lowest);
7 (highest); – – –
Qu Pt Marking Guidance Marks
02 5 Marks are for AO2 (application) 3
1 mark for correct conversion from 00110100 (52) to 11001100 (–52)
1 mark for binary addition of 01101101 (109) to 11001100 (–52) to give
100111001
1 mark for discounting the additional bit on the binary addition to give the final
answer as 00111001 (57)
A. If no other marks awarded, award 1 mark for correct conversion
of 01101101 (109) to 10010011 (-109)
A. Follow through using incorrect representation of –52 for second mark
R. Reject all three marks if decimal subtraction has been used
Qu Pt Marking Guidance Marks
02 6 Marks are for AO2 (application) 2
0101.1100
1 mark for correct integer part
1 mark for correct fractional part
Max 1 if answer not in correct format
How to answer it
Binary Representation & Computer Arithmetic
This exam question evaluates core understanding of data representation and binary arithmetic within AQA AS-Level Computer Science:
- Byte capacity: Calculating the maximum unique values possible with n-bits (2n).
- Unsigned binary: Converting unsigned binary bit patterns into denary (decimal).
- Binary addition: Performing addition with correct carry bit tracking without converting to decimal.
- Two's complement ranges: Determining minimum and maximum representable signed values using n bits (-2n-1 to 2n-1 - 1).
- Two's complement subtraction: Inverting and adding one (finding negative), performing binary addition, and handling the overflow carry bit.
- Fixed-point binary: Splitting fractional numbers into binary whole and fractional parts.
Values Represented by One Byte
1 Mark [AO2]
✅ Correct Answer
256 or 2⁸
💡 Key Knowledge
1 byte = 8 bits. Each bit has 2 possible states (0 or 1). The total number of distinct patterns/values is 28 = 256.
❌ Common Errors
- Writing 255 (255 is the maximum value in an unsigned byte running from 0 to 255, but there are 256 unique values including 0).
Convert 8-Bit Unsigned Binary to Decimal
1 Mark [AO2]
✅ Correct Answer
67
📐 Calculation
Bit pattern: 0 1 0 0 0 0 1 1
- Place values: 128, 64, 32, 16, 8, 4, 2, 1
- Sum = 64 + 2 + 1 = 67
🧠 Exam Technique
Always write the place values (128, 64, 32, 16, 8, 4, 2, 1) directly above the bits to avoid misaligning zeros and ones.
8-Bit Unsigned Binary Addition
2 Marks [AO2]
✅ Correct Answer
Final Answer: 0101 1010
Carry Row: 000 1111 (or carry bits clearly indicated)
📐 Working Out
🧠 Exam Technique
The prompt explicitly requires: "You must show all your working in binary."
- You must write down the carry row.
- 1 + 1 = 0 carry 1
- 1 + 1 + 1 = 1 carry 1
❌ Common Errors
Providing the correct final binary answer without carry bits loses 1 mark because the question demands working to be shown.
• 1 mark for carry row: 000 1111 (carry bits shown in sequence; 0s may be omitted).
• 1 mark for final correct sum: 0101 1010 .
Note: Some working must be shown for any marks to be awarded.
Range of 4-Bit Two's Complement Integer
2 Marks [AO2]
✅ Correct Answer
- Lowest: -8
- Highest: 7 (or +7)
💡 Key Knowledge
In an n-bit two's complement system:
- Most significant bit has negative weight: -2n-1.
- Minimum value: -2n-1 → For 4 bits: -23 = -8 ( 1000 )
- Maximum value: 2n-1 - 1 → For 4 bits: 23 - 1 = 7 ( 0111 )
❌ Common Errors
- Writing -7 and +7 (confusing sign & magnitude with two's complement).
- Giving binary answers instead of decimal (question specifies "Give your answers in decimal").
Subtraction Using 8-Bit Two's Complement
3 Marks [AO2]
Problem: Subtract 00110100 (52) from 01101101 (109).
📐 Step-by-Step Procedure
- Form the negative of 00110100 (-52):
Invert bits: 11001011
Add 1: 11001100 [Mark 1] - Add to the first number (109 + (-52)): 1 1 0 1 1 0 1 1 0 1 (109) + 1 1 0 0 1 1 0 0 (-52) ----------------- 1 0 0 1 1 1 0 0 1 [Mark 2]
- Discard the 9th overflow bit:
Discard leading 1 → 00111001 (57) [Mark 3]
✅ Final Answer
00111001
❌ Common Traps & Examiner Notes
- Automatic 0: Converting to decimal, doing 109 - 52 = 57, and converting 57 back to binary gets 0 marks. The scheme explicitly states: "Reject all three marks if decimal subtraction has been used."
- Leaving the 9th bit: Writing 100111001 as the final answer loses the 3rd mark. It must be truncated to 8 bits.
• 1 mark: Correct conversion of 00110100 to two's complement negative: 11001100 (-52).
• 1 mark: Correct binary addition of 01101101 and 11001100 to produce 100111001 .
• 1 mark: Discarding the overflow bit to give the final 8-bit result: 00111001 .
Fixed-Point Binary Representation
2 Marks [AO2]
Problem: Represent 5.75 as an 8-bit unsigned fixed-point binary number (4 bits integer, 4 bits fractional).
✅ Correct Answer
0101.1100
📐 Step-by-Step Breakdown
- Format: 4 bits before point, 4 bits after → 8 4 2 1 . 0.5 0.25 0.125 0.0625
- Integer part (5): 4 + 1 → 0101 [Mark 1]
- Fractional part (0.75): 0.5 + 0.25 → 1100 [Mark 2]
- Combined: 0101.1100
❌ Common Errors
- Omitting the binary point or providing fewer/more than 4 fractional bits (e.g. writing 0101.11 ). The mark scheme caps at Max 1 if not in the correct specified 8-bit format.
- Miscalculating fractional columns (remember place values halve each step: 0.5, 0.25, 0.125, 0.0625).
• 1 mark for correct integer part ( 0101 ).
• 1 mark for correct fractional part ( 1100 ).
Max 1 mark if answer is not formatted with 4 bits before and 4 bits after the binary point.
Topics
4.5 Fundamentals of data representation · 4.5.2 Number bases · 4.5.3 Units of information · 4.5.4 Binary number system
Question and mark scheme from the AQA A-Level Computer Science examination, AS Paper 2, June 2025. QuestionVault is an independent revision resource; questions remain the copyright of the awarding body.