Storage and transmission

Robert P. Webber and Don Blaheta, Longwood University

 

Computer systems consist of four basic parts: Input devices, output devices, the central processing unit, and secondary storage.

Input devices send data to the computer from the outside world. Common ones are the keyboard, the mouse, and the touchpad. Some systems have microphones. Other input devices, such as sensors, may be used on special purpose computers.

Output devices communicate results from the computer to the user. Most computers have a monitor, speakers, and a printer, for instance. Some systems may have controllers that operate motors or other mechanical devices.

The central processing unit (CPU) is the heart of the computer system. Physically small, the CPU is inside the case that contains the CD drives. On laptops, it is behind the keyboard. All actual computing takes place in the CPU. The CPU has several parts. Random access memory (RAM) temporarily stores data. Read only memory (ROM) holds data that is needed permanently by the system. Registers and the cache are high speed memory. Computations take place in the arithmetic logic unit (ALU). Information is moved around on groups of wires called busses.

Secondary storage devices, such as disk drives, CD and DVD drives, and thumb drives, hold data permanently. Some, such as thumb drives, are portable and can be used to move data between computers. Secondary storage memory is slower for the computer to access than is RAM, but it is permanent, and it can hold far more data than RAM.

The various parts of a computer system are not measured by their physical size, but by how much data they can hold or by the speed with which they operate. Here are some standard abbreviations.

Prefix SI abbrev SI multiplier (base 10) Binary equivalent
Kilo k 1000 (103) 1024 (210)
Mega M 1 million (106) 1,048,576 (220)
Giga G 1 billion (109) 230
Tera T 1 trillion (1012) 240
Peta P 1015 250

Though the standard SI ("Système International", i.e. metric) prefixes are formally defined to indicate powers of ten, we often find it convenient in the computer world to use them to refer to a nearby power of two instead, so for instance a kilobyte (1 kB) usually refers to 1024 bytes. That said, manufacturers will often use whichever meaning will make their product sound more impressive!

Storage capacity is measured in bytes. A byte is exactly 8 bits. (This has been true by definition for decades, although in the early years there were some systems with differently-sized bytes.) Early microcomputers measured their memory in kilobytes (kB). For example, the first Apple II (1977) had 4KB of RAM. The first IBM PC (1981) had 64KB. The Atari ST (1985) was the first popular microcomputer to advertise its memory in megabytes (MB). It came with 1024 KB, or 1MB, of RAM. Today, even the smallest and cheapest computers come with memory measured in gigabytes (GB).

CPU speed is measured in Hertz (Hz). One Hertz is one clock cycle, which is the time the computer takes to do one basic machine operation. Computers work extremely quickly, doing millions, or even billions, of basic operations per second. The first Apple II had a 1 MHz CPU, which meant it could do around 1 million elementary operations per second. That is glacially slow by today's standards. If your CPU is still timed in MHz, you'd better replace it! Modern machines are rated at 1.6 GHz and up.

Secondary storage devices have changed radically over the years, both in type and in storage capacity. Early PCs made use of spinning magnetic media—"disks" or "diskettes"—that measured their capacity in kilobytes. "Zip" disks, mostly with a capacity of 100 MB, were popular for a while.

Few computers today come with diskette drives. Instead, they use CDs, which can hold 682 MB, and DVDs, which can store 4.7 GB. Dual layer DVDs can hold 8.5 GB. thumb drives, also called flash drives or jump drives, can hold from a few MB to hundreds of GB, and their capacities are steadily increasing.

Hard drives, which are internal, sealed disk drives, hold far more information than diskettes or CDs. Their capacity used to be measure in megabytes. Early PC hard drives, in the mid-late 1980s, held 20 MB of data. Today they are measured in gigabytes, with even moderately priced systems having hard drives in the terabyte range.

What does this mean in practice? Suppose you are writing a term paper, for instance. How large will it get? Would we have to worry about whether it would fit in storage?

We'll have to make some assumptions to answer this question. A standard 8 ½ by 11 inch piece of paper consists of 66 lines, each of which is 80 characters long. There will be margins on all sides, of course, and you'll probably double space your paper. Let's assume

Under these assumptions, there will be

33
lines
page
· 50
characters
line
· 1
byte
character
= 1650
bytes
page
.

Suppose the term paper is 15 pages long. Then

15
pages
paper
· 1650
bytes
page
= 24750
bytes
paper
.

A typical cheap thumb drive holds 4 GB, or about 4,000,000,000 bytes. We can obviously fit our paper, which has only 24,750 bytes, onto such a thumb drive. How many such papers could we store on the drive? Notice that if we just naïvely write out our various sizes and numbers, the units don't line up as conveniently as before:

24750
bytes
paper
, 4
GB
drive
, 1000000000
bytes
GB
In particular, two of the terms have bytes in the numerator; so if we just multiply all these numbers we'll get a number with a very strange and un-useful unit. But since the answer to a question like "how many papers fit on the drive?" would have units in the form
papers
drive
, we know we want papers to be in the numerator of its unit. We can invert the unit of a measurement if we also take the reciprocal of the measurement itself: since we have 24750
bytes
paper
, that means that each byte represents a tiny fraction of a paper. Our measurement can become
1
24750
papers
byte
, which lines up nicely with the others:

1
24750
papers
byte
· 4
GB
drive
· 1000000000
bytes
GB
≈ 161616
papers
drive
So we can put more than 160,000 term papers on a 4GB thumb drive! Not every kind of data is so small, though. Music files, in standard format and normally compressed, typically occupy about 1 MB per minute of music. If a typical song runs about 3 minutes in length, that is, 3
minutes
song
, we can line up our units as follows:
1
3
songs
minute
· 1
minute
MB
· 1000
MB
GB
· 4
GB
drive
= 1333⅓
songs
drive

Maybe not enough for a complete music collection, but still pretty respectable.

Exercises

  1. How many times faster is 2 GHz CPU than a 1.2 GHz CPU?
  2. How many times faster is 4.8 GHz CPU than a 2 GHz CPU?
  3. How many times faster is 1.6 GHz CPU than an 40 MHz CPU?
  4. How many times faster is 3.2 GHz CPU than an 800 MHz CPU?
  5. The last Harry Potter book (Rowling:  Harry Potter and the Deathly Hallows, Scholastic, 2007) has 759 pages, with 29 lines per page, and an average of  60 characters per line.

    1.          Could you store this book on a CD? If so, how many books would fit on one disc? If not, how many CDs would it take?
    2.          Same as part a, but use a dual layer DVD.
    3.          Same as part a, but use a 2 GB thumb drive.
  6. The book Sealab (Hellworth: Simon & Schuster, 2012) has 387 pages, with 39 lines per page, and an average of 65 characters per line.
    1. Could you store this book on a CD? If so, how many books would fit on one disc? If not, how many CDs would it take?
    2. Same as part a, but use a single layer DVD.
    3. Same as part a, but use a 16 GB flash drive.
  7. A music file's size is 1900 KB.
    1. How many files of this size could you fit on a CD?
    2. How many files of this size could you fit on a single layer DVD?
    3. How many files of this size could you fit on a 1 GB thumb drive?
  8. Same as problem 7, but you are storing a 662 KB picture file.
  9. Same as problem 7, but you are storing a 2602 KB presentation manager file.
  10. Same as problem 7, but you are storing a 4.53 GB video file.
  11. You want to back up the contents of a 200 MB folder to an external device.
    1. How many CDs would you need?
    2. How many DVDs would you need?
  12. You need to back up the contents of a 350 MB file to an external device.
    1. How many CDs would you need?
    2. How many DVDs would you need?
  13. You need to make external copies of your music files. You have 1200 music files, and they average 6500 KB each.
    1. How many CDs would you need?
    2. How many single layer DVDs would you need?
    3. How many dual layer DVDs would you need?
    4. How many 8 GB thumb drives would you need?
  14. You want to make backup copies of your video files. You have 75 files, and they average 15 GB per file.
    1. How many single layer DVDs would you need?
    2. How many dual layer DVDs would you need?
    3. How many 32 GB flash drives would you need?
  15. How many 40MB audio files could you fit on a 1 TB external hard drive?
  16. How many 4.54 GB video files could you fit on a 1TB external hard drive?
  17. The contents of about how many old "high-density"—that is, 1.4MB—floppy diskettes could be stored on a 1 GB jump drive?
  18. The contents of about how many CDs could be stored on a dual layer DVD?
  19. The contents of about how many CDs could be stored on a 160 GB hard drive?
  20. The contents of about how many dual layer DVDs could be stored on a 320 GB hard drive?
  21. In exercises 21 through 26, you have to store 3000 GB of data.

  22. How many CDs would you need?
  23. How many dual layer DVDs would you need?
  24. How many 2 GB thumb drives would you need?
  25. How many 64 GB jump drives would you need?
  26. How many 512 GB external hard drives would you need?
  27. How many 6 TB external hard drives would you need?
  28. You want to back up the contents of a 3 GB folder from your hard drive to an external device. What external device would you use, and why?

Credits and licensing

This article is by Robert P. Webber and Don Blaheta, licensed under a Creative Commons BY-SA 3.0 license.

Version 2015-Nov-10 02:10