Bits vs Bytes, and the story behind Disk Drive Sizes

By Sareesh Sudhakaran

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Bits

In computer terminology, the bit is the smallest possible thingy – it’s either a 0 or a 1.

A bit is always represented by the small letter ‘b’.

If I’m shooting 8-bit 4:4:4 1080p, then the total number of bits in one frame is 1920 x 1080 x 3 x 8 = 49,766,400 bits. If I’m shooting at 24 frames per second, then the total bits per second = 1,194,393,600 bits per second (b/s or bps).

One can see how talking in bits is tedious. The numbers are too large. What’s next?

Bytes

Scientists discovered pretty early that bits were too small to manage, even back in the early days of computing. For better or for worse, they decided to group 8 bits together, which they called a Byte.

A byte is always represented by the capital letter ‘B’.

One Byte (B) = 8 bits (b)

So, our 8-bit 4:4:4 1080p frame which is 49,766,400 bits is also 6,220,800 bytes. At 24 fps, the data rate is 149,299,200 bytes per second (B/s).

Bits vs Bytes

You’ll find many people using the letters b and B interchangeably, without realizing the ramifications of their ignorance. Even eminent professionals on the internet do this without realizing their mistake.

MBps is not Mbps – They’re two totally different things. If you write one when you mean the other, you are only making it worse for everyone. On wolfcrow, I strictly use the notation MB/s to mean Megabytes per second, while I use Mbps to mean Mega bits per second. I use the ‘/’ notation because some programs (or humans) might be inclined to make everything lower case or upper case while copying or quoting me. At least the ‘/’ will still remain!

Just for the record, if you want to know, in traditional science, one uses the ‘/’ to indicate ‘per’, and avoids the letter ‘p’. On a personal note I hate it when even camera manufacturers and others who should know better continue to use notations like a fifth-grader. It makes their own engineers look bad.

A long time ago bytes were good enough. However, advancements in computer technology ensured bytes were just as ‘unwieldy’ as bits.

Kilobytes

In traditional computing, everything is based on the number 2. To get multiples, the formula is 2n. Even the byte is 8 bits (23 = 8), and not 10.

Traditional science encourages the use of the word ‘kilo’ to mean 1,000. E.g., if 1000 grams (g) is a kilogram (kg), in computing terms, they had to choose a number that could be the result of a direct power of 2.

29 = 512 and 210 = 1024. 1024 was chosen as notation for kilo. Therefore, a kilobyte is not 1000 bytes, but 1024 bytes.

One Kilobyte = 1024 bytes

So, our 8-bit image which is 6,220,800 bytes is also 6,075 kilobytes. At 24 fps, our data rate is 145,800 KB/s. Remember, KB is kilobytes. If you write Kb, it means kilobits.

Megabytes

A megabyte is not 1000 kilobytes, but 1024 kilobytes.

One megabyte (MB) = 1024 kilobytes (KB)

So, our 8-bit image which is 6,075 kilobytes is also 5.93 Megabytes. At 24 fps, our data rate is 142.4 MB/s.

Gigabytes

One gigabyte (GB) = 1024 megabytes (MB)

So, our 8-bit image which is 5.93 Megabytes is also 0.0058 Gigabytes. Obviously, for our purposes, it’s much easier to stop at Megabytes. At 24 fps, our data rate is 0.139 GB/s.

A minute of footage is 8.34 GB. This is how the sizes are used – based on how easy it is to remember or talk about.

Terabytes

One terabyte (TB) = 1024 gigabyte (GB)

So, two and a half hours of our 8-bit 1080p video will need 8.24 x 150 = 1236 GB = 1.2 TB.

All this seems so easy, right? But just as marketing idiots who print brochures with disregard to correct notations are guilty of crimes of omission, some manufacturers could be said to be guilty of crimes of commission.

Imagine this: If I owed you $1,024 but only wanted to give you $1,000, I could call 1,000 1,024. Crazy? That’s what our next topic is about.

SixHardDriveFormFactors

The birth of confusion

First of all, let me make it clear that the full blame for today’s confusion lies both with manufacturers as well as the scientists who ratified these notations.

Most people couldn’t be expected to know or care that computer engineers loved 1024 more than 1000, so people began to use the term kilo like they do with kilograms. Many manufacturers added to this confusion with non-standardized marketing.

Scientists shouldn’t have used the word kilo if they didn’t mean 1000 exactly. Now, half the world cannot talk to the other half because one side means 1000 while the other 1024.

Did somebody try to correct the problem? Sure. They invented new names. Here’s the modern way, also endorsed by the IEEE:

  • Bit is represented as b (lower case).
  • Byte = 8 bits is represented as B (upper case)
  • Kilobyte = 1000 bytes and is represented as kB or KB
  • Megabyte = 1000 kilobytes and is represented as MB
  • Gigabyte = 1000 megabytes and is represented as GB
  • Terabyte = 1000 gigabytes and is represented as TB
  • Petabyte = 1000 terabytes and is represented as PB
  •  
    So, what about the 1024 faction? Computers still can only deal with powers of 2. Therefore, we have a new system for them:

  • 1024 bytes is now a kibibyte (KiB)
  • 1024 kilobytes is now a mebibyte (MiB)
  • 1024 megabytes is now called a gigibyte (GiB)
  • 1024 gigabytes is a tebibyte (TiB)
  • 1024 tebibytes is a pebibyte (PiB)
  •  
    Does this improve matters? Nope. In popular usage, manufacturers and users continue to use the terms interchangeably. It’s hopeless.

    Look at what they’ve done. They’ve called a mile a ‘mili’, while what we all know as a mile is now a new value because a few corporations feel that will better their profit margins. Now, they can claim their cars give more miles per gallon, because the length of a mile has been reduced – officially!

    Thankfully, this crazy scheme hasn’t been widely accepted. There’s still some common sense left in the world.

    Disk Drive Sizes

    Next time you see a hard disk labeled as 4 TB, read the fine print to know whether the manufacturer means 4 TB or 4 TiB.

    What’s the big deal? Look at this:

    4 TB = 32,000,000,000,000 bits
    4 TiB = 35,184,372,088,832 bits

    The difference?

    3,184,372,088,832 bits – or ‘only’ about 398 GB!!

    Can you see the problem? As disk sizes increase, the seriousness of this difference in terminology increases in proportion. Stop taking it lightly. Write to your drive manufacturers asking them to clarify their terms. At the very least, keep this in mind while estimating your disk drive sizes.

    As for this website, I avoid the IEEE notification scheme, and stick to the traditional scheme. Whenever I use kilobytes, megabytes, gigabytes and so on, I’m always using the 1024 system as explained earlier.

    How to calculate the size of an Image

    Let’s say we have an uncompressed TIFF file (or any other raster image/bitmap file). How do we calculate the size per frame?

    Here’s the formula for file/frame size for uncompressed footage:

    Frame size (in bits) = H × V × c × b × s

    Where
    H = horizontal pixels
    V = vertical pixels
    c = number of color channels, almost always 3. Monochrome is 1.
    b = color bit depth in bits
    s = chroma sub-sampling percentage calculated using my formula, expressed as a fraction

    Example One: 1920×1080 16-bit 4:4:4

     Image size

    = 1920(H)x1080(V)x3(c)x16(b)x1(s)

    = 99,532,800 bits

    = 99,532,800 / 8 bytes = 12,441,600 bytes

    = 12.44 MB or 11.87 MiB

    Example Two: 1920×1080 8-bit 4:2:0

    Image size

    = 1920x1080x3x8x0.5

    = 24,883,200 bits

    = 3,110,400 bytes

    = 3.11 MB or 2.67 MiB.

    Example Three: 4096×1716 12-bit 4:2:2

    Image size

    = 4096x1716x3x12x0.667

    = 168,774,009 bits

    = 21,096,751 bytes

    = 21.1 MB or 20.1 MiB

    As you can see, GB is always the bigger number than GiB. Now you understand why manufacturers love them so much.

    Once you have the image size per frame, calculating the data rate is simple – just multiply by the frame rate. To know how RAW files are calculated, check out Deconstructing RAW. To learn how image sizes impacts data rate, take a look at Costs of working with 2K and 4K footage. Knowing this is the first step towards calculating the right disk drive sizes.

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    January 10, 2013

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