Units of information

The reason I wrote this is to clarify something that gets confused all the time. Recently, the Intelligence Squared debates hosted a team to debate net neutrality rules that the FCC recently overturned. I recommend the podcast generally and this debate in particular. There is a lot of confusion around this issue, but this post only covers a small nitpick about units.

In the debate, several people said “10 megabytes per second” or “25 megabytes per second” as their definition of broadband. Those are written as 10Mbps and 25Mbps respectively. ISPs advertise their packages using Mbps, which is “megabits per second”.

Let’s break this down.

the bit

There is no more basic unit of information than the bit, so let’s define it.

1 bit measures the minimum amount of information necessary to answer a single yes/no question.

Notice the qualifier “minimum”, you can answer a yes/no question with the word “yes”, but that’s redundant, you could use “y” as opposed to “n”, but even then, those characters are elements of a set of 26 letters, so they contain more information than we need.

Normally, we use the set of the binary digits {0,1} to denote all possible values of a bit.

In order to represent larger amounts of information, we can start counting using bits.

counting in binary

When we count in decimal, we use the set {0,1,2,3,4,5,6,7,8,9}, and then when we need larger numbers, we pick the next highest digit 1 and count again:

 0, 1, 2...,9, 
10,11,12..,19,
20,21,22..,29,
30,31,32..,39,

We can do the same thing with bits:

  0,   1,
 10,  11,

So summarizing with a table:

decimal binary
0 0
1 1
2 10
3 11
4 100
5 101
6 110
7 111
8 1000
9 1001
10 1010
11 1011

bytes

Computer microprocessors work with larger chunks of bits, most common is the byte.

1 byte = 8 bits

Since there are 8 bits in a byte, that means that a byte can be one of 28 = 256 possible values, because of this, bytes can represent an alphabetic character, a number, or a one of a handful of special characters like %.

The confusion

1MB = one megabyte = 106 bytes = 1,000,000 bytes = 8,000,000 bits

(notice the capital B, thats a convention to denote Bytes)

1Mb = one megabit = 106 bits = 1,000,000 bits

(notice the lowercase B, thats a convention to denote bits)

megabits per second

ISPs like to advertise larger numbers, so saying 8Mbps sounds better than 1MBps, even though those values are the same.

While I knew what the debaters meant, it’s such a common error I felt I needed to clarify this one thing, because it will come up again and again.

Even more confusion

Have you ever noticed your hard drive, USB drive, phone memory having less total space than advertised?

Say you buy a 500GB hard drive, but you plug it in and it says 465.66 GB

What the heck?

Operating systems like Windows or MacOS calculate hard drive space using binary, and hard drive manufacturers use decimal. Since 210 = 1024 ≈ 1000, this is accurate enough not to be a complete scandal.

The explanation then comes down to this: the hard drive manufacturer built a device that can store 500 gigabytes = 500×109 bytes = 500 billion bytes, but when you divide up the space by chunks of 1024 instead of 1000, you get a different number:

500×109 / 230 = 465.661287308

kibibytes, mebibytes, gibibytes, oh my

These are real units that almost no one uses.

1 KiB = 1 kibibyte = 210 bytes = 1024 bytes

1 MiB = 1 mebibyte = 220 bytes = 1,048,576 bytes

1 GiB = 1 gibibyte = 230 bytes = 1,073,741,824 bytes

I don’t blame people for not knowing this one, since the difference between 1MiB and 1MB is so small. However, 1MB and 1Mb are a whole factor of 8 different, and mixing those up is a huge error.

Conclusion

The definition of broadband matters because any policy with real consequences needs a definition. Depending on the definition of broadband, you can either conclude that most Americans have a local monopoly on broadband, or that most Americans have multiple broadband providers. The presence or absence of a monopoly depends on correctly understanding just how much bandwidth we are talking about.

Once that is clear, then we can then have an informed conversation about whether something more needs to be done to regulate ISPs, and if so, what form those regulations should take. Unfortunately, the conversation is dominated by alarmism, talking past each other, trolling, and other harmful forms of dialog.