Thursday - July 02, 2009

Math for Breakfast

In one of my posts the other day I mentioned that I had to do a bit of cleaning up here at the blog, and that I was keeping an eye on space limits. Peiper wrote me about it, so I jokingly replied that he should stop uploading those 20GB pictures of Carla Bruni.

He wrote back with a bit of confusion about megs and gigs and file sizes, so I started writing another one of my computer education email replies back, when I realized, WTH, make a post out of it. So here goes.

Strange, but every number related to computers is done in Base 2, since the heart of a computer is the simple transistor, which is either on (1) or off (0). This leads to some really large, odd looking numbers when you’re talking about larger values, so people have come up common words to express those numbers. These words, prefixes actually, have become common in our language and are used by everyone, even though most people round them off to the nearest power of ten. But computers are very exact, so we won’t do any rounding in this discussion.

8 bits to the byte. 8b = 1B. 1/2 a byte is called a nibble, but nobody uses this term anymore. Nobody hardly even thinks of bits anymore either. Bytes are the common unit of data. All a single bit is, really, is an On/Off switch. You can store some meaning in a byte, but not much. 8 bits limits you to 2⁸ numbers, a mere 256 of them, with the values 0-255. A 32 bit “word” of 4 bytes, or a 64 bit “word” of 8 bytes, is more realistic, but for now we all use bytes as the common size measurement. Units of bits are written as Xb, units of bytes are written as XB. Nuance! Moving right along ...

2¹⁰ bytes = 1024, which is 1 kilobyte, also called 1KB or 1K. For everything other than computers, 1K = 1000.
2²⁰ bytes = 1,048,576, which is 1 megabyte, 1MB. 1M for the rest of everything = 1 million.
2³⁰ bytes = 1,073,741,824, which is 1 gigabyte, 1GB. 1G in common use = 1 billion.
2⁴⁰ bytes = 1,099,511,627,776, which is 1 terabyte, 1TB. 1T of anything else = 1 trillion.

Yes, that’s the American billion. And trillion? Sorry, but I didn’t write the rules. The next larger unit is the petabyte, 2⁵⁰ bytes, 1PB. what we over here call a zillion. This is a number even larger than the total US National Debt. You may insert your own “PETA bites” joke here.

Still with me? Great. Today’s LCD computer monitors are usually in the 16:9 format, which is the width to height ratio. For a 22” diagonal screen of that ratio, this gives you a screen 19.17” wide and 10.79” tall.

The human eye can only distinguish about 3780 x 2485 pixels, which equates to the 1 arcminute (1/60th of one degree) resolving power of the eye on a screen that size. Right now, it looks like Toshiba has a wicked expensive high resolution 22” monitor that does 3840 x 2400 pixels, which is right at the limit of human perception. Awesome. And about $18,000.

Let’s assume price is no object, and that Toshiba has the ability to stitch several of these together to make an ultra-resolution “JumboTron”. Ok. Now let’s assume dear Carla is quite tall, so we’ll need a screen a bit over 6 feet wide to display her life-size, lying down. That means our “UltraTron” monitor would be made from 12 of these smaller ones, 3x4, to give a screen size 32.37” tall and 76.68” wide. I’ll leave it to you to build the graphics card. Anyway, this display would have a resolution of 15,360 x 7200. 110, 592,000 pixels. Call it 110.6Mp.

“Full color” graphics currently means “32 bit color”, which means a pixel can be any one of 2³² colors. 4,294,967,296 colors, to be exact. A 32 bit color bitmap file of a 110.6Mp image works out to a file size of 17,623,131 bytes, which is 16.41GB. Run that file on the quarter million dollar monitor described above and you can look at Carla as large as life and in a level of detail you couldn’t tell from real life.

So, unless you’ve got some larger than life, ultra-detailed photos to upload, don’t worry about it. BMEWS has a mere 1.5GB of storage space, which is plenty enough for the time being.

My first computer was upgraded (!!) from a 10MB to a 32MB hard drive. A good old Seagate ST-4096. It was HUGE! Plus I ran a Perstor card on it, which converted the drive to over 120MB!!!  Beyond massive in those days. 20 years later, right now, for about £55, you can buy a 1TB drive. A terabyte hard drive. For $90. Horry Clap! 1TB is 32,768 (32K) times bigger than 32MB. And the price is a third what I paid back then for the ST-4096, plus the money itself is worth less than half as much. Amazing.

Posted by Drew458     on 07/02/2009 at 11:08 AM   
Filed Under: • Blog Stuff • Science-Technology •  
• Comments (3) • Trackbacks(0)  Permalink •  

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