Units and file size calculations – GCSE Computer Science exam questions with mark scheme

1Grade 1–33 marks

Data is measured in units such as bits and bytes.

(a) State the number of bits in one byte. [1]

(b) State the name of the unit that holds 4 bits. [1]

(a) 8 (bits)(1)
(b) Nibble(1)
(c) 3000 KB; allow 3072 KB (using 1024)(1)
Answer: (a) 8 (b) nibble (c) 3000 KB (allow 3072 KB)
Examiner tip: Learn the order bit → nibble → byte → KB → MB → GB → TB → PB; each step from KB upwards is ×1000.

2Grade 1–33 marks

All data inside a computer, such as text, images and sound, is stored in binary.

(a) Explain why computers store data in binary. [2]

(b) A hard disk drive has a capacity of 1 TB. State this capacity in gigabytes (GB). [1]

(a) A computer is made of (transistors / switches / electronic components) that have only two states, e.g. on and off / high and low voltage(1)
(a) ...so each state can represent one binary digit (1 or 0); accept 'binary only needs two values which is simple / reliable to detect', do not accept 'because computers only understand 1s and 0s' on its own(1)
(b) 1000 GB; allow 1024 GB(1)
Answer: (a) Hardware (transistors) has two states, on/off, which map directly to 1 and 0. (b) 1000 GB (allow 1024 GB)
Examiner tip: 'Computers only understand binary' is circular and earns nothing – link binary to the two electrical states of the hardware.

3Grade 4–54 marks

A student saves a plain-text message containing 2000 characters. Each character is stored using 8 bits.

(a) Calculate the size of the text file in kilobytes (KB). Show your working. [3]

(b) When the student checks the file on disk, it is slightly larger than the answer to (a). Give one reason for this. [1]

(a) 2000 × 8 = 16 000 bits(1)
(a) 16 000 ÷ 8 = 2000 bytes(1)
(a) 2000 ÷ 1000 = 2 KB; allow 1.95 KB (using 1024); award 3 marks for a correct final answer with no working(1)
(b) Metadata is added to the file (e.g. file name / date created / author / character encoding); accept 'the file system stores extra information about the file'(1)
Answer: (a) 2000 × 8 = 16 000 bits = 2000 bytes = 2 KB (b) metadata is stored with the file
Examiner tip: Write the formula bits per character × number of characters first – the method mark survives even if you slip on the unit conversion.

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4Grade 4–54 marks

A small icon is stored as a bitmap image. It is 200 pixels wide and 150 pixels high and uses a colour depth of 4 bits.

(a) State the number of different colours that can be represented with a colour depth of 4 bits. [1]

(b) Calculate the file size of the icon in kilobytes (KB). Ignore metadata. Show your working. [3]

(a) 16 (colours)(1)
(b) 200 × 150 × 4 = 120 000 bits; allow 200 × 150 = 30 000 pixels as part of the working(1)
(b) 120 000 ÷ 8 = 15 000 bytes(1)
(b) 15 000 ÷ 1000 = 15 KB; allow 14.6 KB (using 1024); correct answer with no working scores full marks(1)
Answer: (a) 16 (b) 200 × 150 × 4 = 120 000 bits = 15 000 bytes = 15 KB
Examiner tip: Students often forget to divide by 8 and give 120 KB – label each line as bits, bytes or KB so you can see the step you have missed.

5Grade 6–75 marks

A voice memo is recorded for 10 seconds with a sample rate of 16 000 Hz and a bit depth of 8 bits.

(a) Calculate the file size of the recording in kilobytes (KB). Ignore metadata. Show your working. [3]

(b) The phone has 2 MB of free storage. Calculate the maximum number of seconds of audio that could be recorded with the same settings. [2]

(a) 16 000 × 10 × 8 = 1 280 000 bits(1)
(a) 1 280 000 ÷ 8 = 160 000 bytes(1)
(a) 160 000 ÷ 1000 = 160 KB; allow 156.3 KB (using 1024); correct answer with no working scores full marks(1)
(b) 2 MB = 2 000 000 bytes and one second needs 16 000 × 8 ÷ 8 = 16 000 bytes (or 16 KB); accept 2000 KB ÷ 160 KB per 10 s as an equivalent route(1)
(b) 2 000 000 ÷ 16 000 = 125 (seconds); allow 131 s using 1024 (2 097 152 ÷ 16 000 = 131.07, rounded down)(1)
Answer: (a) 16 000 × 10 × 8 = 1 280 000 bits = 160 000 bytes = 160 KB (b) 125 seconds
Examiner tip: In (b) convert the free space into the same unit (bytes) as the per-second size before dividing – mixing MB with bytes is the common slip.

6Grade 6–73 marks

The diagram shows a 16 GB USB memory stick. A video file of 4.5 GB has already been copied onto it. The rest of the stick is free.

(a) State the amount of free space on the memory stick in megabytes (MB). [1]

(b) Each photo from a camera is 3.2 MB. Calculate the maximum number of whole photos that could be copied into the free space. Show your working. [2]

(a) 11 500 MB; allow 11 776 MB (using 1024)(1)
(b) 11 500 ÷ 3.2 (= 3593.75); allow follow-through from an incorrect (a)(1)
(b) 3593 (photos) – must be rounded down; do not accept 3594 or 3593.75; allow 3680 from 11 776 ÷ 3.2 = 3680(1)
Answer: (a) 11 500 MB (b) 11 500 ÷ 3.2 = 3593.75 → 3593 photos
Examiner tip: A capacity question always wants a whole number of files, and you cannot store part of a photo – round down, never up.

7Grade 8–95 marks

An uncompressed video is made from a sequence of bitmap frames. Each frame is 1280 pixels wide and 720 pixels high with a colour depth of 24 bits. The video plays 25 frames every second and lasts for 1 minute.

(a) Calculate the file size of the video in gigabytes (GB). Ignore sound and metadata. Give your answer to 2 decimal places and show your working. [4]

(b) Explain why videos are normally stored using compression. [1]

(a) One frame = 1280 × 720 × 24 = 22 118 400 bits (= 2 764 800 bytes); allow 1280 × 720 = 921 600 pixels seen(1)
(a) Total bits = frame size × 25 × 60 (or ÷ 8 then × 1500); accept any correct order of operations e.g. 2 764 800 × 1500(1)
(a) = 33 177 600 000 bits = 4 147 200 000 bytes (or 4147.2 MB)(1)
(a) 4.15 GB (accept 4.1472 GB in working); allow 3.86 GB using 1024³; one accuracy mark lost for an answer not to 2 dp(1)
(b) Any one of: an uncompressed video would be far too large to store on a device / to stream or download in a reasonable time / to send as an attachment; accept 'reduces file size so less storage or bandwidth is needed'(1)
Answer: (a) 1280 × 720 × 24 = 22 118 400 bits per frame; × 25 × 60 = 33 177 600 000 bits = 4 147 200 000 bytes ≈ 4.15 GB (b) uncompressed video is too large to store/transmit practically
Examiner tip: Set the calculation out as per-frame → per-second → total; examiners can then award method marks even if a single multiplication goes wrong.

8Grade 4–54 marks

A student looks at four files on their computer. The file sizes are shown in different units.

File	Size
essay.docx	800 KB
song.mp3	0.002 GB
photo.jpg	1.5 MB
clip.mp4	2 500 000 bytes

(a) Write the names of the files in order of size, starting with the smallest. [2]

(b) Calculate the total size of the four files in megabytes (MB). [2]

(a) Converts to a common unit: 800 KB = 0.8 MB, 0.002 GB = 2 MB, 2 500 000 bytes = 2.5 MB (any two correct conversions seen); or an order with only one pair of adjacent files swapped(1)
(a) essay.docx, photo.jpg, song.mp3, clip.mp4 (fully correct order)(1)
(b) 0.8 + 2 + 1.5 + 2.5 (adding four correctly converted values); allow follow-through from (a)(1)
(b) 6.8 MB; allow 6.7 MB using 1024 (0.78 + 2.05 + 1.5 + 2.38 = 6.71)(1)
Answer: (a) essay.docx (0.8 MB), photo.jpg (1.5 MB), song.mp3 (2 MB), clip.mp4 (2.5 MB) (b) 6.8 MB
Examiner tip: Convert everything to the same unit before comparing – a 'bigger number' is not a bigger file when the units differ.

9Grade 8–94 marks

A mono sound file is exactly 1.2 MB in size. It lasts 60 seconds and was recorded with a bit depth of 16 bits. There is no metadata.

(a) Calculate the sample rate, in hertz (Hz), that was used to record the file. Show your working. [3]

(b) The file is re-recorded with the same duration and sample rate but a bit depth of 8 bits. State the new file size in MB. [1]

(a) 1.2 MB = 1 200 000 bytes = 9 600 000 bits (converting file size to bits)(1)
(a) Rearranges the formula: sample rate = file size (bits) ÷ (duration × bit depth) = 9 600 000 ÷ (60 × 16); accept 9 600 000 ÷ 960(1)
(a) 10 000 Hz; allow 10 486 Hz using 1024 (1 258 291.2 bytes × 8 ÷ 960)(1)
(b) 0.6 MB; accept 600 KB; allow follow-through: halving the original size(1)
Answer: (a) 1.2 MB = 9 600 000 bits; 9 600 000 ÷ (60 × 16) = 10 000 Hz (b) 0.6 MB
Examiner tip: Reverse calculations are where marks go – write the forward formula, then rearrange it clearly before substituting; the units line (MB → bits) is a mark on its own.

10Grade 6–74 marks

A designer is choosing a colour depth for a 400 × 300 pixel bitmap image that will be used on a website. The two options are 4 bits per pixel and 24 bits per pixel.

(a) Calculate the file size of the image, in kilobytes (KB), for each colour depth. Ignore metadata. [2]

(b) State how many times larger the 24-bit image is than the 4-bit image. [1]

(a) 4-bit: 400 × 300 × 4 = 480 000 bits = 60 000 bytes = 60 KB; allow 58.6 KB (1024)(1)
(a) 24-bit: 400 × 300 × 24 = 2 880 000 bits = 360 000 bytes = 360 KB; allow 351.6 KB (1024)(1)
(b) 6 (times larger); allow follow-through from (a) values; accept 'the ratio of the colour depths, 24 ÷ 4'(1)
(c) Only 16 colours are available (2⁴) so the image will have lower quality / colours are approximated / banding or loss of detail in photographs; accept a reasoned 'fewer colours so less realistic'(1)
Answer: (a) 60 KB and 360 KB (b) 6 times (c) only 16 colours, so a lower-quality / less realistic image
Examiner tip: In (c) 'worse quality' alone is a half-answer – say why: 4 bits gives only 16 colours so real colours must be approximated.

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