Bits, bytes and the units of storage

Your phone says the film is one point four gigabytes. Your broadband says twenty megabits per second. Both sentences end in a B, and neither means the same thing by it. One counts single ones and zeros, the other counts them in groups of eight, so the two numbers are not even in the same currency.

This video is about how much room a thing takes up. What goes in the room comes next, in C S oh two, oh two, Character sets and ASCII. If binary itself is new to you, start with C S oh one, oh one, Why computers use binary. Search ScholaFly for C S oh one, oh one.

Start at the bottom, with the smallest thing a computer can hold. A bit is one binary digit. It is a zero or a one, and it is the smallest unit of information there is. Eight bits together make a byte. Eight is not an accident: it gives two hundred and fifty six patterns, enough to number every character on a keyboard. Where that count of patterns comes from is worked out in C S oh one, oh two, Denary to binary and back. Four bits, half a byte, is called a nibble. O C R names it and Edexcel lists it, but A Q A never does. Now the piece of notation that quietly decides whether your arithmetic counts at all. So here is your handle for this whole video: little b is a bit, big B is a byte, and when both letters appear in one question there is an eight in the answer. That is the film and the broadband. Megabits is a little b, gigabytes is a capital B. Quick check. A game save is two kilobytes. Working the way A Q A works, how many bytes is that? A, two hundred. B, two thousand. C, sixteen thousand. Take your pick, and hold on to your reason. I'll wait. It is B, two thousand bytes. C is the interesting wrong answer: sixteen thousand is two thousand times eight, so it is the count of bits. Picking C is correct arithmetic answering a different question, and that capital B was the only thing telling you which question it was.

Bytes pile up fast, so the units climb in steps of a thousand, each step with its own name. A thousand bytes is a kilobyte. A thousand kilobytes is a megabyte. A thousand megabytes is a gigabyte. A thousand gigabytes is a terabyte. A thousand terabytes is a petabyte. Every rung is three more zeros. Climbing the ladder you divide by a thousand, and coming back down it you multiply. A Q A takes you as far as terabytes. O C R goes one rung further, up to petabytes, and it does examine that rung. So do a big one now, while the ladder is in front of you. Two thousand terabytes, divided by a thousand, is two petabytes. The bottom of this ladder is where everyone is comfortable and the top is where the errors live, so practise it downwards.

Here is where the three exam boards stop agreeing with each other. A computer does not count in thousands. It counts in powers of two, and the power of two nearest a thousand is one thousand and twenty-four. So there is a second ladder, built on one thousand and twenty-four, and it was given its own names: kibibyte, mebibyte, gibibyte, tebibyte. Count the rungs instead of memorising the powers. A kibibyte is one step up from a byte, a mebibyte two, a gibibyte three, and a tebibyte four, so a tebibyte is one thousand and twenty-four multiplied by itself four times. Operating systems and drive makers have used the two conventions inconsistently for decades, which is exactly why the kibi names were invented. A Q A uses the decimal ladder and only that one, and it states outright that the kibi names are not required. O C R works in thousands by default, and will accept one thousand and twenty-four inside a calculation. Edexcel uses the binary names and nothing else. An Edexcel paper says kibibyte and mebibyte, never kilobyte, and its ladder stops at the tebibyte. So there is no single right answer to what a kilobyte is. Read the unit printed in the question, and answer in that same unit. Take that shopping. One drive is advertised as six terabytes and another as six tebibytes. Same number on the box, one letter different in the word. Which of those two actually holds more? Pick one. I'll wait. It is the tebibyte drive. Six terabytes is six million million bytes, while six tebibytes is six lots of one thousand and twenty-four multiplied by itself four times. That comes to about six point six million million bytes, so the tebibyte drive holds roughly six hundred gigabytes more. The gap widens on every rung you climb, so it is a couple of percent at kilobytes and about ten percent by terabytes.

Now run the whole chain on a question, prefix first and then the factor of eight. How many bits are there in three kilobytes? In that order it is two easy steps, not one awkward one. Step one is the prefix. On A Q A's convention, three kilobytes is three times a thousand, so three thousand bytes. Step two is the factor of eight. Three thousand bytes times eight gives twenty-four thousand bits. So three kilobytes is twenty-four thousand bits, and say both halves out loud: the number, and the unit that number is in. Now the same question for an Edexcel student, working in kibibytes. Three kibibytes is three times one thousand and twenty-four, so three thousand and seventy-two bytes. Times eight, that is twenty-four thousand five hundred and seventy-six bits. Same question, same method, different convention, different correct answer. Go the other way and convert twenty-four million bits into megabytes. Bits into bytes first, so divide by eight, giving three million bytes. Then bytes up to megabytes is two rungs, so divide by a thousand twice. Three million becomes three thousand, then three. So twenty-four million bits is three megabytes, and it stayed tidy because the divide by eight went first. Divide by eight to change the currency, divide by a thousand to change the rung, and every conversion here is those two moves in some order.

Your turn, on the thing the specification actually asks for, which is putting sizes in order. Four quantities are on screen. Nine hundred thousand bytes. Nought point five megabytes. Eight thousand kilobits. And one gigabyte. Smallest first. Convert all four into plain bytes before comparing anything, and look carefully at the third one. Pause the video and work this one through. I'll wait. Nought point five megabytes is five hundred thousand bytes, the smallest. Nine hundred thousand bytes is already in bytes, so it goes next. Eight thousand kilobits is the sharp one, because that is a little b, so it is counting bits. Eight million bits divided by eight is one million bytes. So the order is nought point five megabytes, nine hundred thousand bytes, eight thousand kilobits, then one gigabyte at a thousand million bytes. A glance would have put eight thousand near the top, because it looks big until you notice it is counting bits. Get everything into one unit first and then compare, because quantities still wearing different units cannot be lined up by eye.

The examiner reports on this topic open with good news, so take the good news first. Here is one line from O C R's report on their twenty twenty-two Computer systems paper, about a question where storage units had to be handled. This question was often answered well by candidates who were able to accurately identify the equivalent binary units. So if the ladder made sense to you, or is starting to, you are in good company, because converting units is something students already do well here. Where marks do go is the convention. Edexcel's report on their twenty twenty-four Principles of Computer Science paper puts it in one sentence. Some candidates confused S I units, decimal prefixes, with I E C units, binary prefixes. S I is the thousand ladder and I E C is the one thousand and twenty-four ladder, so that is our two ladders mixed together in a real exam. The same Edexcel report has the factor of eight in it as well. Candidates also struggled to remember that file storage size is in bytes and that transmission speeds are measured in bits, so a conversion factor of 8 is also required. That is the film and the broadband again. Storage is quoted with a capital B, speed with a little b, and an eight always sits between them. One last thing on wording. Both papers examining this content mark precision rather than open-ended analysis, so write the unit next to every number. Right ladder, right convention, right size of letter, and a correct calculation becomes a correct answer on the page.

Little b is a bit, big B is a byte. That line carries most of this video, so here is the run through. A bit is a zero or a one. Eight bits make a byte, and four bits make a nibble. The decimal ladder climbs in thousands: kilobyte, megabyte, gigabyte, terabyte, petabyte. A Q A stops at terabytes, and O C R carries on to petabytes. The binary ladder climbs in one thousand and twenty-fours: kibibyte, mebibyte, gibibyte, tebibyte. Edexcel works in those names and nothing else. And any question that mixes storage with speed has a factor of eight in it, because storage is counted in bytes and speed in bits.

Be honest with the thumb here, because it only does anything for you if it is true. Tap it when big B and little b sort themselves out without you having to stop and think. If the ladder is still slippery, skip the thumb and keep this one saved, then take another run at it before your next test. The ones without a thumb are your to-do list and nothing more. When you are ready to go on, C S oh two, oh two, Character sets and ASCII, puts something inside the room you can now measure.

Next in the chapter: Character sets and ASCII.

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