Speeds and Data Plans

when 1024 is the base multiplier

1024 what?  Where'd you get 1024?

In decimal (base 10), 1 Kilobyte = 1000 bytes

In binary (base 2), 1 Kilobyte = 2¹⁰ = 1024 bytes (1000 * 1.024)

1.25 TB (base 2) = 1250 GB (base 2)

1.25 TB (base 10) = 1250 billion bytes = 1250 GB (base 10)

1.25 TB (base 2)  = 1250 billion * 1.024 = 1280 billion bytes = 1280 GB (base 10)

1.25 TB (base 2) = 1280 GB (base 10) because Cox is mixing two, different bases.

The individual who drafted verbiage for the Cox webpage might have only been told monthly data plans are to have a 1.25 TB data limit.  If so, assuming it was a binary amount may or may not have been correct.  Either way, the "1,280 GB" was probably included to provide a more relatable decimal GB amount, but base mixing made it confusing.  The monthly data limit is most likely 1.25 TB binary (1280 GB decimal), but clarification from Cox would be needed to confirm that .  

base mixing made it confusing

It can be confusing...but an erroneous $10 penalty would quickly clarify.

2^10 does equal 1024.  1024 what?  1024 bits.  One thousand & twenty-four 1's and 0's.  1024 is an expression of the binary numbering system:  1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, etc.

However, as soon as you started notating as "bytes," you departed the binary numbering system by dividing the binary expression with 8.  Whenever we notate as kB, MB, GB, TB, PB, EB, ZB, YB, etc...it's base-10.

However, as a side note, if you want to remain within the binary numbering system to express big numbers, you must use binary prefixes:  KiB, MiB, GiB, TiB, PiB, EiB, ZiB, YiB, etc.

This is where you went wrong:  1.25 TB (base 2)  = 1250 billion * 1.024 = 1280 billion bytes = 1280 GB (base 10)

• Because of the "B," 1.25 TB is not a binary expression (base-2)
• 1.25 TB does = 1250 billion in the decimal numbering system
• However, you multiplied the base-10 expression (1250) by a kilobit'd base-2 expression (1.024) to get an erroneous hybrid value (1280).

Why multiply...just use 1 system.

I understand this is highly trivial, maybe even nonsensical, to some readers.  For example, if we're comparing kilobits to kilobytes, the numerical difference is a paltry 2.4%.  Who cares, right?  However, when we venture into the "tera" territory (sorry), the differences get significantly greater.

At which point would Cox start "automatically" charging $10:  1.25 TB or 1280 GB?  If Cox penalized you at 1.25 TB, you'd have a legitimate gripe because you hadn't reached 1280 GB.  Maybe the $10 is trivial.

This has devolved into another stupid conversation.  

2^10 does equal 1024.  1024 what?  1024 bits.

There are 1024 bytes in a kilobyte (KB) using conventional metrics.

This is where you went wrong:  1.25 TB (base 2)  = 1250 billion * 1.024 = 1280 billion bytes = 1280 GB (base 10)

• Because of the "B," 1.25 TB is not a binary expression (base-2)
• 1.25 TB does = 1250 billion in the decimal numbering system
• However, you multiplied the base-10 expression (1250) by a kilobit'd base-2 expression (1.024) to get an erroneous hybrid value (1280).

1.25 TB (base 2)  = 1250 billion * 1.024 = 1280 billion bytes = 1280 GB (base 10)

The above statement is accurate.  You misinterpreted it.  It was included as-is to to maintain a standard presentation with the other methods listed.  Base 2 indicates the calculation is based on a binary KB with 1024 bytes.  The references are to amounts of data transmitted, not transmission rates.  TB is appropriate to represent an amount of data, regardless of the base used in the calculation.   

A binary KB is 1024 bytes and a decimal kilobyte is 1000 bytes.  My calculation determined the decimal equivalent of a single binary byte by dividing the size of a binary KB by the size of a decimal KB.  1024/1000 = 1.024.  I then multiplied the 1.024 factor by the size of decimal 1.25 TB (1250 billion bytes) to get the 1280 GB size of 1.25 TB with a binary KB.

1000 * 1000 * 1000 * 1000 * 1.25 = 1250 Billion bytes (using decimal KB)

1024 * 1000 * 1000 * 1000 * 1.25 = 1280 Billion bytes (using binary KB) 

1024/1000 = 1.024  * 1250 Billion = 1280 Billion bytes (using binary KB)

You get to the same place either way, but using the binary to decimal ratio highlights a binary KB is 1.024 times larger than a decimal KB.

MB calculation methods

Base 10: 1000 * 1000 = 1,000,000 bytes         International Standard of Units (SI)  

Mixed:    1024 * 1000 = 1,024,000 bytes         Conventional metrics  

Base 2:   1024 * 1024 = 1,048,576 bytes         Computer storage

Cox used conventional metrics that report a larger amount than the more accurate decimal measure.  But, we don't know if the webpage is accurate or if it's just how the webpage author interpreted the specs.

Conventional metrics

KB = 2¹⁰ = 1024 bytes

MB = 1000 KB = 1,024,000 bytes not 1 * 1,000,0000 = 1,000,000 bytes

GB = 1000 MB= 1,024,000,000 bytes

TB = 1000 GB= 1,024,000,000,000 bytes

Data Units Converter

www.gigacalculator.com/.../data-storage-bandwidth-converter.php

With the "Use SI standard" box unchecked (conventional metrics), enter 1.25 in the box on the left and select TB, then select GB on the right. 1.25 TB = 1,280 GB 

Now check the "Use SI standard" box (decimal)                          1.25 TB = 1,250 GB 

Well...I was spending my time researching a cheaper data plan.

Do you think the Cox legal team would have a calculator?

How does 1.25 TB equal 1280 GB?

Data Units Converter

www.gigacalculator.com/.../data-storage-bandwidth-converter.php

With the "Use SI standard" box unchecked (conventional metrics), enter 1.25 in the box on the left and select TB, then select GB on the right. 1.25 TB = 1,280 GB 

Now check the "Use SI standard" box (decimal)           1.25 TB = 1,250 GB 

I don't think you read my reply.  It's not a question of math or conversion.  It's a grammatical or notational question.

1. Why convert?  Does the average subscriber read or understand binary storage?

2. If you need to convert, use the concise notation of said conversion:  1280 GiB.  "B" is understood as decimal and "iB" binary.

3. If you need to convert, convert all the established limits listed on the page.

A kilobyte has always been 1024 bytes,  Not knowing that makes it obvious you don't have a programming background.  You still don't understand what I tried to explain to you.

There is a technical and a general specification of kilobyte.  However, the #1 rule of communications:  analyze your audience.  To whom is Cox communicating with on this page...programmers or everybody?

There are 2 systems to notate storage:  base-10 and base-2.  The IEC has completely standardized and notated storage for both systems up to the power of 8 (yottabyte and yobibyte).  This system distinguishes "B" as base-10 and "iB" as base-2.  Your reference (JEDEC) is base-2 but incomplete, limited and confusing because it also uses "B" as does base-10.  Is 1280 GB base-10 or -2?  Does Cox expect us to do some math?

I fully understand your post, but it wasn't a question about from where or how you get 1280 GB.  I understand and appreciate your effort; however, it's a question of why use 1280 GB.

If it's a standard practice for Cox to bill storage as base-2, great...fantastic...tag it and footnote it.  However, Cox just notated as 1280 GB and left it to our imagination.  What happens if I consume 2 TB or data in 1 month?  How would you, Curt, notate this size...2 TB or 2 TiB?  As far as I know, JEDEC can't express in tera.  JEDEC may have updated to YB...I don't know...but why not just distinguish base-2 with an "iB" notation?

You're original question was 

Monthly data plan.  How does 1.25 TB equal 1,280 GB?  Do you mean 1.28 TB or 1,250 GB?  At which threshold would Cox start "automatically" charging $10 for exceeding a data plan:  1.25 TB or 1,280 GB?  It's only a difference of 30 GB or 2 UHD movies.  Why can't Cox be "StraightUp" with us?

How 1.25 TB = 1280 GB has been explained enough.

You're other concern was losing 30 GB of data.  So I'll back out of the 1280 to get you to the 1250 you want to see.  (This should look familiar.  I'm just going in the other direction than in the earlier post).

1024 * 1 billion * 1.25 = 1280 Billion

1000 * 1 Billion * 1.25 = 1250 Billion

1024/1000 = 1.024   

1280 Billion / 1.024 = 1250 Billion

For the math to work, we've determined that the 1280 GB referenced is actually 1280 Billion bytes.  1280 GB is 1310.72 Billion bytes.  The website author probably failed to make that distinction (or didn't expect anybody to fact check it).  But if you were expecting a 1250 Billion byte data limit, you're getting an extra 30 Billion bytes.

See?  You're not losing any data.  Had Cox simply omitted the "(1,280 GB)", you would have been fine.  Ironically, including that bit of explanation appears to have been Cox trying to be "StraightUp" with us.

A kilobyte is and will always be 1024 bytes because computers can more easily calculate 2¹⁰ than add up individual bytes.  You can look it up.  There are a few bazillion websites that mention it.