Computer Data Storage

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• Computer Data Storage
• (Internal Representation) Chapter 1
• Winter 2005

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Summary

• A flip-flop is a means of storing a bit in an
  electronic circuit.
• Gates are electronic circuits which can be used
  to build a flip-flop or other circuits which
  perform addition of bits, etc.
• The gates AND, OR, XOR, and NOT are examples of
  Boolean operators.
• In actual circuits a 1 corresponds to an on
  voltage (usually 3.2 volts or 5 volts) while a 0
  is off, or 0 volts.

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Sect. Main Memory

• The principle reservoir of memory (places to hold
  bits) is called main memory.
• Main memory is arranged in cells, typically of
  size 8 bits, or 1 byte. These are arranged in
  consecutive order, each cell having its own
  address.
• The computer can access these cells through a
  read operation, or a write operation, in any
  order (random access memory or RAM)
• The total number of cells is arranged in powers
  of 2 Usually in kilobytes (KB), megabytes (MB),
  gigabytes(GB), terabytes, . . . These are 1024
  bytes (210), 1,048,576 bytes (220), 1024 MB
  (230), etc.

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Main Memory cont

• Within each cell we assign an order to the bits
  one side is the most significant bit
  (high-order end) and the other is the least
  significant bit (low-order end, i.e. the 1s
  column).

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Sect. 1.3 Mass Storage

• RAM is the working memory of a computer. Its
  not often large (64 to 256 MB typically) and
  isnt maintained while the computer is turned
  off. But, it is typically fast (? nanoseconds or
  1x10-9seconds)
• Mass storage is also a reservoir of places to
  store bits only it is typically large (40GB is
  common now) permanent, not lost while power is
  off, and slow (? milliseconds access times 1x10-3
  seconds) often requiring mechanical motion to
  access memory (i.e. a hard drive).

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Mass Storage cont

• Magnetic disks (hard drive)
• Similar to magnetic cores but instead of small
  doughnuts now we use magnetic material on a hard
  disk. Bits are written along a circular track by
  a read/write head which is a mechanical arm.
  When a new track is written, the head moves to a
  new cylinder. Each track is divided into arcs
  called sectors. Each track within a particular
  disk system contains the same number of sectors
  and each sector contains the same number of bits.
  Typically a sector is 512 bytes. (Sometimes also
  called a block.)
• When we decide where the cylinders,tracks and
  sectors are we are said to have formatted the
  disk.

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Mass Storage cont

• Disk storage systems can be either hard disk or
  floppy disk. This just refers to the type of
  disk used. Typically hard disks have multiple
  hard disks arranged in a stack, each with its own
  read/write head.
• A disks performance is measured in terms of 1)
  seek time (time required to move the head from
  one track to another), 2) rotation delay or
  latency time (half the time required for the disk
  to make a complete rotation), 3) access time (the
  sum of seek time and rotation delay), and 4)
  transfer rate (rate at which data can be
  transferred to or from the disk).

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Other Forms of Mass Storage

• Compact disks
• CD-DA (compact disk - digital audio)
• CD-ROM (compact disk - read-only memory) 650MB
• DVD - ROM (digital versatile disk - read only
  memory) 10 GB
• DVD - RAM (digital versatile disk - random access
  memory)
• Magneto-optical disk (200MB - 4 GB)
• Magnetic Tape (25 GB) (typically used for
  backing up systems)

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Other Storage Techniques

• Magnetic cores
• Used in very early computers and in military
  electronics.
• Data is not lost when the power is turned off
• Magnetic cores arent as easily destroyed by an
  airburst nuclear explosion (EMP)
• Capacitors
• Either charged or discharged
• Must be refreshed many times per second --
  dynamic memory (DRAM)

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File Storage and Retrieval

• Information is stored on mass storage systems as
  files. i.e. a complete document, image, email,
  etc.
• Mass storage systems manipulate whole sectors.
  When referring to this block of information on
  the disk we call this a physical record. A file
  will then typically be made up of many physical
  records (will be recorded over many sectors).
• Groups of data (files) are then further divided
  into logical records.
• Buffer
• Fragmentation
• Virtual memory

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Machine Architecture(The ideas which allow us to
compute)

• How do we store information on a piece of
  Silicon?
• Digital versus Analog information
• Encoding of data (decimal,binary, hexadecimal)
• How do we manipulate that data?
• i.e. how can we add two numbers

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Digital Analog Information

• Computers are digital -- What does that mean?
• Digital information is
• Robust (easy to handle without errors)
• Low noise
• Example Digitization of audio
• Audio digitization software (SoundView for the
  Mac -- http//www.physics.swri.edu/SoundView/Sound
  View.sit.hqx)

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The process for digital audio goes something like
this At the recording studio
analog signal digitized sound 5 7
3 0 7 9 encode to binary
010101110011000001111001 record bits on
CD burning a CD On your CD
player read bits on CD 01010111001100000111
1001 decode 5 7 3 0
7 9 play sound analog signal
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• Bit -- A binary digit
• A box which can hold only the values 0 and 1

Bits are easy to store on CDs as tiny pits, or
spots, burned by a laser.
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Binary Counting

• 0
• 1 1 one 1
• Out of digits, must carry
• 10 1 two , 0 ones 2
• 11 1 two, 1 one 3
• Out of digits in 2s column, carry
• 100 1 four, 0 twos, 0 ones 4
• 101 1 four 0 twos 1 one 5
• 110 1 four, 1 two, 0 one 6

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• Binary Numbers for 0-15 decimal

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Binary to Integer conversion
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(No Transcript)
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Integer to Binary conversion figs. 1.15 and
1.16 Step 1 Divide the value by two and record
the remainder. Step 2 As long as the quotient
obtained is not zero, continue to divide the
newest quotient by two and record
the remainder. Step 3 Now that a quotient of
zero has been obtained, the binary
representation of the original value consists of
the remainders listed from right to left in the
order they were recorded.
(This is an algorithm)
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• Characters
• Characters correspond to letters or symbols
• ASCII code look-up table (Appendix A, p. 539)
• (space) 00100000
• ! 00100001
• 00100010
• .. ..
• W 01010111
• and so on .
• Hello 01001000011001010110110001101100011011
  11

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Operations on Bits

• We would like to be able to compare bits
• logical operations
• AND, OR, NOT, XOR
• We need to be able to add bits

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Storing a bit

• Storing a bit within a machine requires a device
  that can be in one of two states. Weve seen how
  to do this on a CD, namely with a pit burned by a
  laser. This, however, is permanent.
  Furthermore, you cant flip a bit in order to,
  say, compute the 2s complement, or add two
  binary sequences. A computer must have available
  a means of both storing a bit and changing it.

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More than couple bits

• Hello 010010001100101011011000110110001101111001
  01110
• Long and confusing - humans can only handle small
  sets of bits
• Hexadecimal system allows easier reading of bit
  patterns
• Base 16

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Section 1.1 Storage of Bits
Value 4-bit Hex.
0 0000 0 1 0001 1 2 0010 2 3 0011 3 4 0100 4 5 010
1 5 6 0110 6 7 0111 7 8 1000 8 9 1001 9 10 1010 A
11 1011 B 12 1100 C 13 1101 D 14 1110 E 15 1111 F

• Is there an easier way to write all those 1s
  and 0s?
• Yes -- Hexadecimal notation
• (base 16)

Example 2 byte (16-bit) 0010 0111 1111
0001 ? D70B ?
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Hexadecimal cont

• 1100010 8 bit
• 1100 0100
• C 4
• 1100010010101111 16 bit
• 1100 0100 1010 1111
• C 4 A F
• 11000100101011110011010111100110 32 bit
• 1100 0100 1010 1111 0011 0101 1110 0110
• C 4 A F 3 5
  D 6

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Sect. 1.5 The Binary System

• Lets take a closer look at the Binary System

Addition Rules of addition 0 1 0
1 0 0 1 1 0 1 1 1 0 see fig.
1.17, p. 45
Adding two numbers using binary patterns (dont
say binary numbers because binary sequences can
correspond to characters, which you could add as
well)
This is a carry, not a ten
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Half Adder
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Storing fractions in binary

• Radix point
• Plays the same role as the decimal point in
  decimal notation
• Addition is carried out the same as for binary
  sequences representing integers (just align the
  radix points).

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Sect. Storing Integers

• (How to represent positive and negative integers
  at the same time)
• Twos Complement Notation
• a method compatible with digital circuitry
• negative numbers

3-bit
3 011 2 010 1 001 0 000 -1 111 -2 110 -3 101 -4 10
0
If the left most bit is a 1 then it represents a
negative number
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Examples of 2s Complement Representation

• Starting with the binary representation of a
  positive integer, find the representation of its
  negative counterpart.
• Copy and flip method
• 1s Complement and add 1 method
• Addition in 2s complement
• Subtraction in 2s complement
• Overflow errors

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Storing non-integers

• Weve seen how to represent integers (i.e. whole
  numbers), characters, and fractions by binary
  sequences. Now we look at how to represent
  non-integer numbers in binary.
• Floating point numbers are numbers like 5.234 or
  0.127
• For larger or smaller numbers we use scientific
  notation or engineering notation

123456.9 1.234569 x 105
1.234569E5 -0.0001234 -1.234 x 10-4
-1.234E-4
sign mantissa exponent
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Floating point numbers (cont)
123456.9 1.234569 x 105
1.234569E5 -0.0001234 -1.234 x 10-4
-1.234E-4
sign mantissa exponent
The exact way we represent the mantissa and
exponent can be complicated. The algorithm used
depends on the precision required. Typically we
have either 32 or 64-bit sequences. We wont go
into the details here.
8-bit binary sequence
The binary sequence is broken up into 3 sections.
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Full Adder
Abstraction
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Add 4 bits
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Sect. Communication Errors

• Any time we have multiple computers or multiple
  devices that are connected by cables, wires or
  radio waves we must transmit binary sequences in
  order to transfer information. Environmental
  factors such as dirt, water, electrical
  interference (including sunspots!) are
  unavoidable. These can cause errors to arise in
  the transmission.
• What can we do about these errors?

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Communication Errors cont

• Create a scheme where we can detect errors.
• Add to this a scheme where we can correct errors.

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Parity Bits

• One way of detecting errors is to add a parity
  bit to a sequence of bits.
• For example, consider an odd parity system
• For each binary sequence add one bit. This bit
  is a 1 if there are an even number of 1s in the
  original binary sequence. Make this bit a 0 if
  there are an odd number of 1s.
• The point is to make every binary sequence have
  an odd number of 1s.
• After transmission we check the parity of the
  incoming sequences. If any sequence has an even
  number of 1s (even parity) then we encountered
  an error.
• Q If all received sequences have odd parity can
  we be sure no errors occurred?

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Error Correcting Codes

• Q Can we correct a message with errors in it
  even if we dont know the original message?
• Yes, to an extent.
• Hamming distance
• First, create a code. This code has the property
  that every member is represented by a binary
  sequence that is different from all the other
  members in a special way. Each member has a
  Hamming distance of at least 3. The Hamming
  distance is the number of bits in which two
  binary sequences differ, column by column. See
  example.
• http//www.princeton.edu/matalive/VirtualClassroo
  m/v0.1/html/lab2/lab2_5.html
• Second, encode your information using this code.
• Transmit your data

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Error Correcting Codes, cont

• Decode the data using the code. If any one
  sequence doesnt match to a legal binary sequence
  in the code, an error has occurred.
• Finally, to correct the error we compare the
  received code with the code table. If we find
  that our received code differs by one bit from a
  legal sequence then we assume this legal
  sequence, which represents a certain character,
  is what was originally sent -- so we substitute
  it in.
• This last step assumes that only 1 error
  happened. But there are ways of solving this
  problem too. We can simply increase the Hamming
  distances between all members of our code. That
  way we could account for more errors.