OCR GCSE Computer Science Computer systems (01), June 2025: Question 5
10 marks · Medium difficulty · Calculation
Perform unit conversions, number base conversions between denary, 8-bit binary, and hexadecimal, 8-bit binary addition, and binary shifts.
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Question text
(a) Tick (✓) one box to identify the quantity of megabytes that is the same as 2 terabytes.
2000 MB
20 000 MB
200 000 MB
2 000 000 MB
[1]
(b) Each row in the table contains a number that is written as a denary value, 8-bit binary value and
a 2-digit hexadecimal value. Some values are missing.
Complete the table by writing in the missing value for each number.
Denary 8-bit binary 2-digit hexadecimal
38 26
01001110 4E
156 10011100
215 D7
14 [4]
(c) Complete the binary addition of these two 8-bit binary numbers.
Show your working out.
01 1 1 0 0 1 1
+ 0 0 1 1 0 1 0 0
[2]
(d) Tick (✓) one box to identify the result of a 2-place right binary shift on the binary number
01110111.
00011101
11101110
00111011
11011100
[1]
(e) Describe the binary shift that can be used to multiply any number by 8.
… [2]
Mark scheme
Show the mark scheme
Question Answer Mark Guidance
5 (a) 1 mark for 2000000MB (last one) 1
5 (b) 1 mark for each completed box 4 Correct answers only
Denary 8-bit Binary 2-digit Hexadecimal – binary must be 8
bits.
38 00100110 26
78 01001110 4E
156 10011100 9C
215 11010111 D7
5 (c) 1 mark for working all 3 carries. 2 Do not award
1 mark for binary answer conversion to denary
e.g. as the only working.
01 1 1 0 0 1 1
+ 0 0 1 1 0 1 0 0
10 1 0 0 1 1 1
11 1
5 (d) 1 mark for 00011101 (first one) 1
5 (e) 1 mark each 2 No marks for
• Left shift contradictions e.g.
• 3 places “shifting to left or right”
How to answer it
Data Representation: Units, Conversions, Addition & Binary Shifts
This question covers fundamental Component 01 (Data Representation) topics:
- Converting storage capacity units (Terabytes to Megabytes using 1000/1024 base prefixes).
- Converting between Denary, 8-bit Binary, and 2-digit Hexadecimal.
- Performing 8-bit binary addition showing correct carries.
- Executing and describing logical binary shifts to perform multiplication and division.
Part (a) — Storage Units Conversion
Identifying equivalent Megabytes in 2 Terabytes
✅ Correct Answer
Tick the 4th box: 2 000 000 MB
📐 Step-by-Step Calculation
- GCSE OCR uses base-1000 for standard unit prefixes:
1 TB = 1 000 GB - 1 GB = 1 000 MB
- Therefore, 1 TB = 1 000 × 1 000 = 1 000 000 MB
- For 2 TB:
2 × 1 000 000 = 2 000 000 MB
❌ Common Errors
- Missing zero counts: Choosing 20 000 MB or 200 000 MB by multiplying by only 100 or 10 000 instead of jumping two full steps of 1000.
- Confusing Gigabytes and Megabytes (2 000 MB is only 2 GB).
Part (b) — Number Base Conversions
Filling the gaps: Denary, 8-bit Binary, and Hexadecimal
✅ Completed Conversion Table
| Denary | 8-bit Binary | 2-digit Hexadecimal |
|---|---|---|
| 38 | 00100110 | 26 |
| 78 | 01001110 | 4E |
| 156 | 10011100 | 9C |
| 215 | 11010111 | D7 |
📐 How Each Value is Calculated
- Row 1 (Binary for 38):
38 = 32 + 4 + 2 → 00100110 (Or convert hex 2 = 0010 , 6 = 0110 ). - Row 2 (Denary for 01001110 / 4E):
Hex: (4 × 16) + 14 (E) = 64 + 14 = 78.
Binary: 64 + 8 + 4 + 2 = 78. - Row 3 (Hex for 10011100):
Split into nibbles: 1001 and 1100 .
1001 = 9, 1100 = 12 (Hex letter C) → 9C. - Row 4 (Binary for D7):
D = 13 = 1101 , 7 = 0111 → Combine: 11010111 .
❌ Common Errors
- Writing only 6 bits (e.g. 100110 instead of 00100110 ). The question explicitly demands 8-bit binary!
- Hex digit slip: Thinking E is 15 (it is 14; F is 15).
- Writing denary in the hex column, such as writing 912 instead of 9C .
Part (c) — 8-bit Binary Addition
Adding two 8-bit binary numbers with working shown
✅ Full Working & Final Answer
+ 0 0 1 1 0 1 0 0
-----------------
1 0 1 0 0 1 1 1
1 1 1 ← (carries)
• 1 mark: Showing all 3 carries clearly.
• 1 mark: Correct final binary sum: 10100111 .
🧠 Exam Technique: Carries
- Always write carry bits underneath or above the addition columns.
- Rules:
• 1 + 0 = 1
• 1 + 1 = 0 (carry 1)
• 1 + 1 + 1 = 1 (carry 1) - Warning from Examiner: Do NOT simply convert the numbers to denary, add them, and convert back. You will lose the method mark because no binary carries are demonstrated.
Part (d) — Right Binary Shift
2-place right shift on 01110111
✅ Correct Answer
Tick the 1st box: 00011101
📐 Step-by-Step Shift
- Original: 0 1 1 1 0 1 1 1
- Shift right by 1 place: 0 0 1 1 1 0 1 1 (the last 1 drops off)
- Shift right by 2nd place: 0 0 0 1 1 1 0 1 (another 1 drops off)
- Fill empty places on the left with zeros.
Part (e) — Describing a Shift to Multiply by 8
Describing the direction and number of places
✅ Correct Description
- Left shift (1 mark)
- 3 places (1 mark)
💡 Key Knowledge: Shifts as Powers of 2
- Left shift: Multiplies by 2n (where n is the number of places).
- Right shift: Integer division by 2n.
- To multiply by 8:
8 = 2³
Therefore, you must shift Left by 3 places.
❌ Common Errors & Examiner Warnings
- Contradictions: Writing vague responses such as "shift left or right by 3" earns 0 marks.
- Confusing shifts with the multiplier: Stating "shift left 8 places" (which would multiply by 2⁸ = 256, not 8).
- Wrong direction: Saying "right shift 3 places" divides by 8 instead of multiplying.
Topics
1.2 Memory and storage · 1.2.3 Units · 1.2.4 Data storage
Question and mark scheme from the OCR GCSE Computer Science examination, Computer systems (01), June 2025. QuestionVault is an independent revision resource; questions remain the copyright of the awarding body.