GCSE · Computer Science · AQA · Spec 8525

Gigabyte (GB)

A 750,000 kB video. 0.8 GB of free space. 750,000 against 0.8 looks hopeless, but the two numbers are in different units. So will it fit?

Computer Science · Units of data

Where does each file land?

This line counts megabytes (MB), from 0 to 2,000 MB. That's 0 to 2 GB, because 1 GB = 1,000 MB. And 1 MB = 1,000 kB. Convert each file size into MB in your head, then drag it to where it belongs.

A — 0.4 GBB — 750,000 kBC — 0.8 GBD — 1,250 MBE — 1.6 GB

Computer Science · Units of data

How many bytes in a gigabyte?

A kilobyte is 1,000 bytes: a 1 followed by 3 zeros. Next up the ladder comes mega, then giga. Written out in bytes, one gigabyte is a 1 followed by how many zeros?

Your estimate

8 zeros

A kilobyte is 1,000 bytes: a 1 followed by 3 zeros. Next up the ladder comes mega, then giga. Written out in bytes, one gigabyte is a 1 followed by how many zeros? Estimate between 0 zeros and 15 zeros.

0 zeros15 zeros

Computer Science · Units of data

Convert, then compare

Which is more data: 2.5 GB or 2,400,000 kB?

Put both into the same unit. MB sits between GB and kB, so each needs just one rung.Any shared unit works. MB keeps the arithmetic short.
missing step

Which line is step 2?

2.5 GB into MB: MB is the smaller unit, so divide by 1,000. 2.5 ÷ 1,000 = 0.0025 MB.2.5 GB into MB: MB is the smaller unit, so multiply by 1,000. 2.5 × 1,000 = 2,500 MB.2.5 GB into MB: MB is the smaller unit, so multiply by 100. 2.5 × 100 = 250 MB.

Computer Science · Units of data

Bits or bytes?

Is each of these measured in bytes or in bits? Look at the very last letter.

Still to sort

Bytes (B) (0)

Capital B. A byte is a group of 8 bits.

Where the line is: A capital B means bytes, whatever prefix sits in front of it.

Bits (b) (0)

Lowercase b. A bit is a single 0 or 1, the fundamental unit of information.

Where the line is: A lowercase b means bits. 8 of them make one byte, so the same number in bits is 8 times less data.

6 of 6 still to sort.

The prefix in front says how many. The last letter says of what.

Watch out: Only the final letter decides bits or bytes. The prefix letter just sets the size, so kB and kb are both "kilo", but they are not the same amount.

Computer Science · Units of data

So is it 1,000 or 1,024?

Ask around and you'll hear different answers to one simple question.

How many megabytes are there in 1 gigabyte? Pick the one closest to what you think right now.

1,024 MB. Computers work in binary, so it must be a power of 2.1,000 MB. Each step up the ladder is × 1,000.100 MB, like 100 centimetres in a metre.1,000,000 MB. Giga means a billion, so it's a massive number.

How sure are you?

I'm sureI think soI'm guessing

1,024 MB. Computers work in binary, so it must be a power of 2.

This is a common misconception

You've probably seen 1,024 somewhere, and there's a real reason for it. Historically, the names kilobyte, megabyte and so on were often used for powers of 2, and 2¹⁰ (ten 2s multiplied together) is 1,024. But kilo, mega, giga and tera are SI prefixes, and SI prefixes are based on powers of 10. With these decimal prefixes, 1 GB is 1,000 MB.

1,000 MB. Each step up the ladder is × 1,000.

This matches the evidence

Yes. Giga, mega, kilo and tera are decimal prefixes based on powers of 10, and each one is 1,000 times the one below. So 1 GB = 1,000 MB, just as 1 MB = 1,000 kB and 1 TB = 1,000 GB.

100 MB, like 100 centimetres in a metre.

This is a common misconception

Centi is a different prefix. These prefixes go up in jumps of 1,000, the same kilo you know from 1 kilometre = 1,000 metres. Mega, giga and tera carry on the same way, so 1 GB = 1,000 MB, not 100.

1,000,000 MB. Giga means a billion, so it's a massive number.

This is a common misconception

Giga does mean a billion, but a billion BYTES, not a billion megabytes. From GB down to MB is only one rung, so it's × 1,000 once. The 1,000,000 you're thinking of is how many kilobytes are in 1 GB: two rungs down.

With the decimal prefixes, 1 GB = 1,000 MB. If you meet 1,024, that's the older powers-of-2 habit. Use 1,000.

WHAT YOU'VE LEARNED

A quick recap of today's lesson.

Every step up the prefix ladder is × 1,000. Put two sizes into the same unit and comparing them becomes easy.

What you need to know

What a bit and a byte are, and how they're related
What the symbols B and b stand for
The decimal prefixes kilo, mega, giga and tera, and their symbols
That 1 GB is 1,000 MB (and that 1 MB is 1,000 kB and 1 TB is 1,000 GB)
How to convert between prefixes, and which way round to do it
How to compare quantities of bytes written with different prefixes

The big picture

A bit is the smallest unit of information: a single 0 or 1. A byte is a group of 8 bits, and we write B for byte and b for bit. Large quantities of bytes use decimal prefixes: kilo (k), mega (M), giga (G) and tera (T). Each one is 1,000 times the one before, so 1 MB is 1,000 kB, 1 GB is 1,000 MB and 1 TB is 1,000 GB. That makes a gigabyte a billion bytes. To compare two quantities written with different prefixes, convert them into the same prefix first, then compare the numbers.

Key points

1A bit is the fundamental unit of information: it is either a 0 or a 1.

2A byte is a group of 8 bits. B stands for byte and b stands for bit.

3Kilo (k), mega (M), giga (G) and tera (T) are decimal prefixes. They are SI prefixes, based on powers of 10.

4Each prefix is 1,000 times the one below: 1 MB = 1,000 kB, 1 GB = 1,000 MB and 1 TB = 1,000 GB.

5So 1 GB is 1,000,000,000 bytes: a billion bytes, or 10⁹.

6Going to a smaller unit (GB → MB), multiply by 1,000 for each rung. Going to a bigger unit (MB → GB), divide by 1,000 for each rung.

7To compare quantities with different prefixes, convert them into the same prefix first, then compare the numbers.

8Historically, kilobyte, megabyte and so on were often used for powers of 2, which is where 1,024 comes from. With the decimal prefixes, 1 GB = 1,000 MB.

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Worked example

Problem

Put these storage sizes in order, smallest first: 0.3 TB, 320 GB, 290,000 MB.

⚠ Watch out

Comparing the numbers and ignoring the prefixes. 900 MB looks bigger than 1.2 GB because 900 is bigger than 1.2, but 1.2 GB is 1,200 MB, so it's the bigger one. Convert to the same unit before you compare.

🧠

Memory hook

k, M, G, T: every step up is three more zeros. And the Big B is a Byte; the little b is just a bit.

✓

Check yourself

Without looking back: which is more data, 0.07 TB or 65,000 MB? Say which unit you converted into, whether you multiplied or divided, and why.

Flashcards

(12)

What is a bit?

The fundamental unit of information. A bit is either a 0 or a 1.

What is a byte?

A group of 8 bits.

What do the symbols B and b stand for?

B stands for byte. b stands for bit.

Name the four decimal prefixes in order, smallest first, with their symbols.

kilo (k), mega (M), giga (G), tera (T).

How many kilobytes are in 1 megabyte?

1,000 kB.

How many megabytes are in 1 gigabyte?

1,000 MB.

How many gigabytes are in 1 terabyte?

1,000 GB.

How many bytes are in 1 gigabyte?

1,000,000,000 bytes: a billion, or 10⁹.

What are SI prefixes such as kilo and mega based on?

Powers of 10.

Converting between prefixes: when do you multiply by 1,000, and when do you divide?

Multiply for each rung down to a smaller unit (GB → MB), because you need more of them. Divide for each rung up to a bigger unit (MB → GB), because you need fewer.

How do you compare two quantities written with different prefixes?

Convert them into the same prefix first, then compare the numbers.

Where does the number 1,024 come from?

Historically, kilobyte, megabyte and so on were often used for powers of 2 (2¹⁰ = 1,024). With the decimal prefixes, 1 GB = 1,000 MB.

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Where does each file land?

How many bytes in a gigabyte?

Convert, then compare

Bits or bytes?

So is it 1,000 or 1,024?

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