Megabytes, gigabits and googolplex – what’s in a number?

It’s all geek to me!

This post started life as a question from someone – who shall remain nameless(!)  – when downloading some software onto their tablet. I paraphrase:

Is a gigabyte more than a megabyte?

Firstly the meaning of the prefixes; here’s a quick ready-reckoner for the most common multipliers that you will hear with respect to technology, including:

• Computer memory size (internal to your device, external physical devices or cloud-based storage)
• Upload and download internet speeds (data transfer rates)…read all about your broadband here
• The speed of the your computer/device (as a microprocessor or chip speed), often used as an indicator of the processing ‘power’

(Source. http://searchstorage.techtarget.com/definition/Kilo-mega-giga-tera-peta-and-all-that)

A lot of the prefixes have Greek roots, hence the awful pun at the start of this article.

Looking at the ‘Power of 10’ column:

• Kilo/K or k, pronounced ‘kay’ means thousands, 10³ being 10x10x10 or 1,000 (3 zeros)
• Mega/M  or simpler ‘Meg’ means millions, 10⁶ is 1,000,000 (6 zeros)
• Giga/G or ’Gig’ means billions*, 10⁹ is 1,000,000,000 (9 zeros)
• Etc.

(*Ed Be careful though, when politicians and economists refer to a billion they usually mean 100 million – this started as an American-English anomaly but is now commonplace)

You get the picture, a nice neat sequence with each multiplier being a thousand times bigger or smaller than it’s neighbour, all the way up to 10²⁴ and down to 10^-24 (tiny amounts that we do not need to go into now). There are more exotic huge numbers, including a ‘googol’ which is 10¹⁰⁰, such an improbably large number that mathematicians and scientists describe it in terms of the age of the universe in seconds and comparisons of the weight of the universe compared to a single electron…both of which are still a lot smaller than a googol. There is also a bigger number, the googolplex, but don’t worry these are not coming to PC World or your broadband supplier in the near future.

(Ed. Did you know that Google is an accidental misspelling of googol, the aspiration of the founders to provide access to a lot of information)

Base 2

As a brief digression I need to explain the ‘power of 2’ column. You may be aware that all computers work with data stored as binary states (1/0, on/off etc.)

A bit – shortened from ‘binary-digit’ – is the smallest piece of recordable information, but you can’t do much with something that can only have 2 values, until you start putting them together in large numbers. For example 8 bits (2-to-the-power-of-8), traditionally called a byte lets you code (give a numerical value to)  up to 256 things, enough for example to code the western alphabet, the digits 1 to 10 with quite a few left for punctuation, and various control characters, i.e. 1 byte holds one piece of information.

So a ‘k’ or ‘K’ can refer to 1,000 (base 10) or 1,024 (base 2), not enough difference to be worried about, its enough to know that 1 Kbytes allows the storage of 1 thousand characters, give or take, 1 MByte gives use access to 1 million characters etc.

For comparison, think of a typical book with say 250 pages each holding 2,000 characters (including spaces), we are talking in the region of 500,000 characters (500K or 0.5M)

According to the Telegraph the average UK broadband speeds is 18.7Mbps (bits per second) – of course us rural dwellers get nothing like this!

Multiplying  bytes x 8 to get bits means your book of 4M bits can be downloaded in under 5 seconds! I am massively simplifying for raw ‘plain text’ here. Data stored and transmitted is normally a lot more complex and resource-hungry, including richer web pages, high resolution pictures and video. For example:

• The average size of a web pages is over 1,500K/1.5M*
• Quite a modest 5 megapixels picture needs about 2MB storage (compressed)
• A one minute high definition video file will eat up 16GM

(*Ed. all figures as at October 2015, more or less, who knows what the demand and the technology will look like in 2 years or even 2 months time!)

I haven’t talked about the prefix ‘tera’ in the table, but we are starting to see Terabyte storage available for personal use, normally as cloud-based capacity or physical back-up devices. A million million bytes is an incredible amount of space, but no doubt individuals (video, pictures) and particularly businesses will increasingly take it for granted. Which brings me quite neatly on to Moore’s Law, stated by Gordon Moore c.1970, to the effect that;

 [micro] processor speeds, or overall processing power for computers will double every two years.

Doubling being an increase of the power-of-2.  Similar incredible changes can be seen in the size of memory and network/internet speeds, so maybe we need to get used to a few more the multipliers (peta-, exa-, yotta-?) ,  and more complicated maths, in our life-time!

Need to know

Back to the question, you should now know that a ‘Gig’ is 1,000 times more than a ‘Meg’, so all other things being equal a 1 GByte file will take 100 times longer to download than a 10 Megabyte file. And a 256k (256,000 bytes of data per second) dial-up modem is just too slow – ask your dad!

So it wasn’t a daft question, people need to know these things and feel able to ask without fear of either ridicule or being confronted by more confusing jargon and technobabble. The IT Elementary School is all about making the confusing understandable.

You remember when you were at school and you were told that you would need maths (or ‘math’ in the US) in everyday life, well here’s a case where a little bit of applied knowledge is useful.

IT Chemist

@ITelementary

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