Size Matters

The question with two right answers

Most of this topic is settled and exact. A nibble is four bits. A byte is eight bits. Nobody argues about that, on any exam board. It is the prefixes that people disagree about, and this specification handles that disagreement in an unusual way that is worth knowing before you meet it in a question. One exam board tells its students to work in thousands. Another tells its students to work in 1024s. This specification gives one as the default and then explicitly says the other is acceptable as well. ⚠️ So on this paper, "how many bytes in a kilobyte" genuinely has two defensible answers, and the mark is not for picking the right one. The mark is for saying which convention you are using, and then not changing your mind halfway through the answer. That is the whole skill on this topic, and almost nobody arrives knowing it.

The units, and which are in dispute

The first three are fixed. The last two are the two ways of handling everything above a byte.

Two conventions, both accepted

Read the third column carefully. It is the part that makes this paper different from the other boards, and it is the part revision videos will not tell you.

How to answer when either is allowed

Being allowed to choose sounds easier than being told what to do. It is not, because it puts the responsibility on you, and there is a small routine that discharges it. Say which convention you are using, in words, before you calculate anything. One short sentence at the top of the answer is enough, and it costs you nothing. Then use that one for every step. Not most steps. Every step. And show the working, so whoever marks it can follow the choice you declared rather than guessing at it. ⚠️ Here is why that routine is worth the seconds it takes. An answer that names its convention and applies it consistently is markable even if the marker would personally have chosen the other one. An answer that starts with one and finishes with the other is wrong under both of them, however carefully each individual sum was done. Consistency is doing more work here than accuracy.

Match each unit to what it is

Two answers, and how to give one

On this paper you are asked how many bytes there are in a kilobyte. What is the best way to answer?

• Give 1,000 and say you are using the decimal convention, or give 1,024 and say you are using the binary one. Either is accepted when you name it
• Give 1,000, because it is the only figure this specification allows
• Give 1,024, because computers work in powers of two so 1,000 is always wrong
• Give both numbers, without saying which one you would use

Why the drive looks smaller than the box

Buy an external drive, plug it in, and the size the computer reports is noticeably less than the size printed on the box. Nothing is faulty. No space is missing. Nothing has been taken by the file system. The two figures are the same amount of storage, counted two different ways. The manufacturer counted in thousands. The operating system counted in powers of two. Same drive, two conventions, two numbers. ⚠️ That is this whole topic, happening in the world rather than in a textbook, and it is the reason your specification refuses to declare either habit wrong. Storage makers count the way every other measurement prefix counts, which is entirely reasonable. Computers address memory in powers of two, which is also entirely reasonable. Both habits are older than any exam board and neither is going away. ⚠️ So the move to take into the exam is this: never write that somebody's conversion is wrong because they used the other convention. Say which convention was used. That is a stronger observation and it is the one that earns marks on this paper.

Bytes in the file, counted in thousands

Using the decimal convention, where one kilobyte is 1,000 bytes, work out how many bytes there are in a file of 4 kB.

The same file, counted in 1024s

Now take exactly the same 4 kB file, but use the binary convention, where one kilobyte is 1,024 bytes. Work out how many bytes there are this time.

Smallest to largest

Put the units in order, smallest first. The order is the same whichever convention you use, which is worth noticing.

• A bit
• A nibble
• A byte
• A kilobyte
• A megabyte
• A gigabyte
• A terabyte
• A petabyte

Complete the data units paragraph

A single binary digit, either 0 or 1, is a _____. Four of them together make a _____, and eight of them make a _____. The convention this specification gives as its default treats one kilobyte as _____ bytes, but it also accepts the convention that treats one kilobyte as _____ bytes.

Units at speed

Five in a row, three lives. The first three are the parts nobody argues about.

Spot the true data units facts

Tap the TWO statements that are true.

• A nibble is four bits and a byte is eight bits
• This specification accepts either 1,000 or 1,024 bytes to the kilobyte, provided you say which you used
• A conversion that uses 1,024 is marked wrong on this paper
• The order of the units from smallest to largest changes depending on which convention you use

Three unit calls

Three situations. Choose the response you could defend in writing.

• A student converts the first half of an answer using 1,000 and the second half using 1,024. Every individual sum is done correctly. What is the problem?
• A classmate revising from another board's material insists that 1,000 is the only correct figure and that anything else loses marks. What do you tell them?
• Someone buys a drive advertised at one size, plugs it in, and the computer reports noticeably less. What has actually happened?

Explain the units and the two conventions

A friend has been told by someone at another school that half of what they learned about data units is wrong. Write them the answer that sorts it out.

• Name the units this specification uses, from the smallest upwards
• State how many bits are in a nibble and in a byte, and say why those figures are not in dispute
• Explain the two conventions for the prefixes and what this specification says about each of them
• Explain what you have to do in an answer so that either convention is markable
• Finish by explaining why a drive can be advertised as one size and reported by a computer as another