4.5.3 Units of Information — AQA 7517

Bits and Bytes

All data in a computer is stored as binary digits (bits). Groups of bits form the units we use to measure data storage and transfer.

Unit	Size	Notes
Bit	1 binary digit (0 or 1)	Smallest unit of data
Nibble	4 bits	Half a byte; one hex digit
Byte	8 bits	Stores one ASCII character

SI Prefixes vs Binary Prefixes

Two systems exist for measuring larger data quantities:

Decimal (SI) prefixes — powers of 10

Prefix	Symbol	Value	Bytes
Kilobyte	KB	10³	1,000 bytes
Megabyte	MB	10⁶	1,000,000 bytes
Gigabyte	GB	10⁹	1,000,000,000 bytes
Terabyte	TB	10¹²	1,000,000,000,000 bytes
Petabyte	PB	10¹⁵	1,000,000,000,000,000 bytes

Binary (IEC) prefixes — powers of 2

Prefix	Symbol	Value	Bytes
Kibibyte	KiB	2¹⁰	1,024 bytes
Mebibyte	MiB	2²⁰	1,048,576 bytes
Gibibyte	GiB	2³⁰	1,073,741,824 bytes
Tebibyte	TiB	2⁴⁰	≈ 1.1 trillion bytes

Why the discrepancy?

Hard drive manufacturers use SI (decimal) prefixes to make drives seem larger. Operating systems traditionally use binary calculations. A "500 GB" drive may appear as ~465 GiB in an OS.

Data Transfer Rates

Transfer rates measure how quickly data moves between devices. Units are expressed per second:

Unit	Full name	Typical use
bps	bits per second	Modem speeds, serial connections
Kbps	kilobits per second	Old dial-up (56 Kbps)
Mbps	megabits per second	Broadband (100 Mbps)
Gbps	gigabits per second	Ethernet, USB 3.0

Note: Network speeds use bits (lowercase b), not bytes. 100 Mbps = 100 ÷ 8 = 12.5 MB/s download speed.

Calculating Storage and Transfer

File size calculation

For a bitmap image: width (px) × height (px) × colour depth (bits) ÷ 8 = file size in bytes

Transfer time calculation

Transfer time (s) = File size (bits) ÷ Transfer rate (bps)

Exam tip: Know the difference between decimal prefixes (KB=1000 bytes) and binary prefixes (KiB=1024 bytes). Network speeds use bits per second (lowercase b); storage uses bytes (uppercase B). 8 bits = 1 byte — always divide by 8 to convert between bits and bytes. Be ready to calculate file size in bytes and transfer time.

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Worksheet — 4.5.3 Units of Information

8 questions · instantly marked · AQA 7517 standard

Q1How many bits are in a byte, and how many bytes are in a nibble?[2]

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8 bits in a byte [1]; a nibble is 4 bits, which is half a byte (0.5 bytes) [1].

Q2Explain the difference between a kilobyte (KB) and a kibibyte (KiB).[2]

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Kilobyte (KB) = 1,000 bytes — uses SI/decimal prefix (power of 10) [1]; kibibyte (KiB) = 1,024 bytes — uses IEC/binary prefix (2¹⁰) [1].

Q3A broadband connection has a speed of 80 Mbps. A user downloads a 400 MB file. How long will the download take? Show your working.[3]

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Convert file size to bits: 400 MB × 8 = 3,200 Mb = 3,200,000,000 bits [1]; convert speed to bps: 80 Mbps = 80,000,000 bps [1]; time = 3,200,000,000 ÷ 80,000,000 = 40 seconds [1].

Q4A bitmap image is 1920 × 1080 pixels with 24-bit colour depth. Calculate the uncompressed file size in megabytes. Show your working.[3]

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Total bits = 1920 × 1080 × 24 = 49,766,400 bits [1]; total bytes = 49,766,400 ÷ 8 = 6,220,800 bytes [1]; in MB = 6,220,800 ÷ 1,000,000 = 6.22 MB (or 5.93 MiB using binary prefix) [1].

Q5Why do hard drives appear to have less storage capacity than advertised when connected to a computer?[2]

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Manufacturers advertise using SI (decimal) prefixes where 1 GB = 1,000,000,000 bytes [1]; operating systems measure in binary prefixes (1 GiB = 2³⁰ ≈ 1,073,741,824 bytes), so the same drive appears smaller — e.g. a "500 GB" drive shows as ~465 GiB [1].

Q6A sound file stores 3 minutes of audio at 44,100 Hz, 16-bit, stereo. Calculate the uncompressed file size in MB. Show working.[3]

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Duration = 3 × 60 = 180 seconds; samples = 44,100 × 180 × 2 (stereo) = 15,876,000 [1]; bits = 15,876,000 × 16 = 254,016,000 bits [1]; bytes = 254,016,000 ÷ 8 = 31,752,000 bytes ≈ 31.75 MB [1].

Q7A network speed is stated as 1 Gbps. How many MB/s is this?[2]

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1 Gbps = 1,000,000,000 bits per second [1]; divide by 8: 1,000,000,000 ÷ 8 = 125,000,000 bytes/s = 125 MB/s [1].

Q8State the number of bytes in: (a) 1 GB (SI), (b) 1 GiB (binary). Why does this matter in computing?[3]

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1 GB (SI) = 1,000,000,000 bytes [1]; 1 GiB (IEC binary) = 2³⁰ = 1,073,741,824 bytes [1]; this matters because storage is often sold in SI units but OS reports in binary units, causing apparent discrepancies in capacity [1].

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Bits and Bytes

SI Prefixes vs Binary Prefixes

Decimal (SI) prefixes — powers of 10

Binary (IEC) prefixes — powers of 2

Why the discrepancy?

Data Transfer Rates

Calculating Storage and Transfer

File size calculation

Transfer time calculation

Worksheet — 4.5.3 Units of Information

Mini Test — Units of Information