Chapter 1: Machine Architecture

1
Chapter 1 Machine Architecture

• CS as science
• science requires the construction of theories
  which are confirmed or rejected by
  experimentation
• sometimes theories are dormant because technology
  is not yet available to test them
• in other cases, current technology influences the
  theories
• In CS, both of these have been true
• neural network theories laid dormant for 20 years
  while hardware caught up to them
• cheap processors are influencing the development
  of modern Artificial Neural Networks

2
The Machine

• Central to Computer Science is the algorithm
• But it is the computer that allows us to
  experiment, test our algorithms
• So it is important to understand this machine so
  that we understand how it will influence our
  algorithms and theories
• Here, we will concentrate on the representation
  of information in binary
• In the next chapter, we will examine how the
  machine manipulates and processes this
  information

3
Binary

• 1 bit (binary digit)
• a 0 or a 1
• Basic unit of storage for a computer
• We use binary because of the nature of digital
  circuits
• A circuit is either in an on state (1) or off
  state (0)
• Examples
• Flip Flop
• circuit that continuously stores an electrical
  current or no electrical current until a new
  input causes its state to change
• Relay
• in one of two physical positions
• Magnetic core
• stores a magnetic charge in one of two directions
• Capacitor
• stores a magnetic charge or no magnetic charge
  (for a short duration)

4
Gates and Logical Operations

• Electronic circuits that perform a logical
  operation
• Based on boolean algebra
• Often called Boolean operations (see the gates on
  p. 20)
• AND -- output is 1 if both inputs are 1
• OR -- output is 1 if either inputs are 1
• NOT -- output is 1 if input is 0
• XOR -- output is 1 if inputs differ
• These 4 operations form the basis for all
  computer operations!

5
Circuits Built with Gates

• Flip-flops combine 3 logic gates
• AND, OR, NOT
• Look at the flip-flop in figure 1.3, p. 21 and
  the examples of setting and clearing the
  flip-flop in figure 1.4 p. 22
• The Flip-flop is perfect for storing 1 bit
• Half Adder (or 2-bit adder)
• Adds together 2 binary bits, 00, 01, 10, 11
• Uses two logic gates, an AND gate (for carry out)
  and an XOR gate (for sum)
• Full Adder
• Combines Half Adders together by connecting the
  Carry Out of one to the Carry In of another
• Forms a chain of Adders, n Half Adders to add 2
  n-bit numbers

6
More on Adders

• Adding two bits
• a b
• SUM computed by a XOR b
• CARRY OUT computed by a AND b
• Adding n sets of two bits
• a1 a2 a3 a4 an b1 b2 b3 b4 bn
• For a given two bits, say ai bi and a previous
  CARRY IN, C,

• SUMi NOT (ai) AND NOT (bi) AND C OR NOT(ai)
  AND bi AND NOT (C) OR ai AND NOT(bi) AND
  NOT (C) OR ai AND bi AND C
• CARRYi ai AND bi AND C OR ai AND bi AND
  NOT(C) OR ai AND NOT(bi) AND C OR NOT(ai)
  AND bi AND C
• The first Full Adder will have a CARRY IN of 0
  (hardwired into it)
• The last Full Adder will have a CARRY OUT that
  leads to the overflow bit (well talk about this
  later)

a1 b1 a0 b0
CarryIn0
Adder
Adder
Carry
Carry
Sum1 Sum0
7
Types of Memory

• For a computer to work, it needs storage for the
  current instruction and current data
• There are many types of memory, each different in
  speed and cost, with the faster memory costing
  more so there is less of it in the computer
• This forms a memory hierarchy
• Registers -- fast memory stored in the CPU made
  out of flip-flops
• we will look at the CPU and registers in the next
  chapter
• Cache -- expensive, nearly as fast as registers
• Main memory -- cheaper, slower, made out of
  capacitors
• Secondary storage -- very cheap, very slow

8
What to store?

• In the earliest computers, storage was only used
  for data
• Von Neumann conceived of the idea of a stored
  program
• place the program in the same memory as data
• This allowed computers to have flexibility
• no need to hard code the program
• And speed
• no need to input program instructions from an
  external source while executing the program
• Programs and data are both stored in binary

9
Main Memory

• Think of main memory as a very long set of
  mailboxes where each box can store 1 item
• Each cell can be written to or read from
• Reads are not destructive, so its more like a
  copy

• Repository for program instructions and data
• Large collection of circuits, sometimes called
  cells
• each capable of storing 1 byte (8 bits)
• 8 bits can store 28 256 different combinations
  of 1s and 0s
• each memory location has a unique address (a
  number)

10
Some Memory Terminology

• Types of memory
• Volatile memory - requires power to retain its
  contents
• memory made out of flip-flops and capacitors are
  volatile
• Random Access Memory (RAM)
• memory that can be accessed by address (most
  memory is RAM)
• volatile memory
• RAM is readable and writable
• Read Only Memory (ROM)
• main memory that is readable but not writable
• made of different hardware than flip-flops and
  capacitors
• non-volatile memory

• Storage Capacities
• 1 byte 8 bits
• 1 kilobyte (1KB or 1K) 1024 bytes (210 bytes)
• 1 megabyte (1MB or 1M) 1024 kilobytes
  (approximately 1 million bytes or 220 bytes)
• 1 gigabyte (1GB or 1 G) 1024 megabytes
  (approximately 1 billion bytes or 230 bytes)

11
Storage Devices

• Main memory
• limited in size due to cost
• volatile
• Additional storage is required
• Secondary storage devices (mass storage) is
• non-volatile, cheap (compared to main memory) and
  long-term (years to decades at least)
• These devices are added on to the computer
• Require physical motion of parts and therefore
  are slower and more liable to fail
• Types magnetic disk, optical disk, magnetic tape

12
Magnetic Disk

• Most common form of storage
• A disk of either flexible or rigid material with
  magnetic coating that can store magnetic charges
• Disk spins around and read/write head of drive
  reads/writes magnetic charges on disk
• Multiple disks form a platter where each surface
  has its own read/write head, where they all move
  together over the same track, called a cylinder

• Disk composed of tracks and sectors
• Tracks and sectors are created when the disk is
  formatted (often in the factory these days)

13
More on Magnetic Disk

• A directory (file allocation table) stores the
  location of a file on the disk
• Location -- cylinder, track, sector
• Read/Write head now accesses the file
• Seek time -- time for R/W head to move to proper
  track
• Rotational delay (or latency time) -- time for
  R/W head to wait for proper sector to move under
  it
• Access time -- sum of Seek time and Rotational
  delay
• Transfer time -- rate at which data can be
  transferred
• Typically, a file is broken into individual
  blocks scattered across the disk, so the R/W head
  will have to move from one block to another,
  lengthening the access time

14
Types of Magnetic Disks

• Floppy
• slow, cheap, portable
• 1.44 Megabyte of storage
• R/W head touches the surface of these disks
• Zip
• removable like floppies, but sealed like hard
  disks
• offers a compromise in price and capacity (100
  Megabytes)

• Hard
• disk enclosed with drive, not removable
• multiple disk platters
• offers up to 10 Gigabyte of storage
• each platter has its own R/W heads
• More expensive than floppy
• but prices are much cheaper today than 5 or 10
  years ago, much faster than floppy disks
• R/W head glides above/below disk surface
• If the R/W head touches the disk, its called a
  head crash and can permanently damage the disk
  and head

15
Two More Storage Devices

• Optical Disks
• Information stored as burn marks over a
  reflective surface
• Information read by laser
• Once written, disks cannot be erased or rewritten
• CD-ROM -- information comes on the disk from
  factory
• WORM -- blank disk, written once, read only
  afterward
• Optical disks offer
• portability
• large storage capacity (740MB)
• relatively cheap but not erasable
• Other optical technology does offer erasable disk
• Variations of optical disks include CD-DA
  (digital audio) and DVD (digital versatile disk)

• Magnetic Tape
• Oldest form of storage
• Magnetic charges placed on tape much like on disk
• Access is sequential leading to very slow access
  times and therefore inefficient compared to disk
• Offers large storage capacity for cheap cost
• Not used much today, mostly backups and archives
• Types reel-to-reel, cassette, video, DAT,
  high-speed tape cartridge

16
Units of Storage

• In main memory, we refer to bytes
• In mass storage, we refer to files
• Files are broken up into blocks and distributed
  across the disk
• usually, files are placed wholly on tape and
  unbroken
• Since secondary storage access is slow compared
  to main memory, it is common for storage devices
  to have buffers (RAM)
• Or access RAM directly to temporarily store
  information in memory buffers

17
Binary Representations

• Now that we know how information is stored in the
  computer and storage devices, we need to
  determine how to represent our information using
  binary
• need representations for
• text (characters)
• integer numbers (both positive and negative)
• fractions and real numbers
• program code
• pictures, sounds, music

18
Text and ASCII

• ASCII
• Most common text representation, used by all PCs
  and most other computers
• Each character is stored in 1 byte using ASCII
• Need codes for
• Upper case letters, lower case letters, 10
  digits, punctuation marks, various keyboard
  commands
• Example
• H 01001000
• e 01100101
• l 01101100
• o 01101111
• . 00101110
• Hello 01001000 01100101 01101100 01101100
  01101111 00101110

• In 1 byte, we have 256 different combinations of
  1s and 0s
• Lets assign each combination to be a code that
  uniquely identifies one character
• Codes
• ASCII American Standard Code for Information
  Interchange using 7 bits (128 combinations)
• Unicode newer method using 16 bits (65,536
  combinations)
• ISO 32 bits (17 million combinations)

19
Representing Numbers

• In decimal, each digit represents a unit
  multiplied by a power of ten
• 375 3 100 7 10 5 1
• In binary, units multiplied by a power of 2
  where each unit is a 0 or a 1
• 101010012 127 026 125 024 123
  022 021 120 1283281 169
• We have columns for 1s, 2s, 4s, 8s, 16s, etc

• We similarly can have 1/2s column, 1/4s column,
  etc on the opposite side of the decimal point for
  fractions
• Example 01100.100 is 12.5 in decimal
• To convert from binary to decimal
• Sum up each (digit 2i where digit 1 or 0, and
  i is the position or column of the digit)

20
Converting from Decimal to Binary

• Given the decimal value
• Divide the value by 2 and record the remainder
• As long as the quotient is not 0, continue
• The binary value is the list of remainders in the
  order they were obtained, listed from right to
  left
• Example 13
• 13/2 6 with a remainder of 1
• 6/2 3 with a remainder of 0
• 3/2 1 with a remainder of 1
• 1/2 0 with a remainder of 1
• Or, 13 11012

21
Representing Negative Numbers

• Our previous binary representation only stores
  positive numbers
• We could assign the first bit to be the sign bit
• if it the leading bit is a 1, then the number is
  negative, if the leading bit is a 0, then the
  number is positive
• Example 3 is 00000011, -3 is 10000011
• This has two drawbacks
• there are two ways to represent 0 (10000000 and
  00000000) so that 8 bits can only represent 255
  different numbers
• we have to be careful when adding numbers to not
  add the sign bits of the two numbers
• A better representation is twos complement

22
Twos Complement

• The first bit is still a sign bit
• But here, the entire number is different if
  negative
• For instance, 3 00000011, but -3 is not
  10000011
• To obtain the twos complement version
• Start from the right side and copy the number
  down exactly until you reach the first 1, then
  negate each bit to the left after that first 1
• 3 00000011, -3 is formed by working from right
  to left, leaving the first 1 bit alone, but
  inverting all remaining bits or those underlined
  in the following 00000011
• Giving 11111101
• To convert back to the positive version, apply
  the same technique giving 00000011

23
More on Twos Complement

• Advantages of 2s Complement
• Twos complement has only one way to represent 0,
  00000000
• so that 8 bits can store 256 different numbers
• When adding Twos Complement numbers, we no
  longer have to worry about the sign bit
• In fact, subtraction becomes simplified
• X - Y becomes X (-Y)
• That is, negate Y and add the result to X
• So we dont need a subtraction circuit, just an
  adder and a negation circuit
• See figure 1.21 on page 50
• Notice that a positive number is the same whether
  represented using 2s complement or unsigned
  binary or signed magnitude binary

24
Overflow

• Notice that a carry out of the last bit in a
  binary addition is an overflow
• 100100 gt 127 and so causes an overflow
• The CPU monitors the last carry out for such
  circumstances
• However, with a positive and negative number, the
  carry out is not an overflow
• So, an overflow occurs if the sign bit of the
  result ! the sign bit of the 2 numbers
• Example 0011 1110 1 0001 no overflow
  since sign bit of the two numbers differ
• Example 1100 1010 1 0110 overflow since
  the sign bit of the result differs from the sign
  bits of the two numbers
• Example 1100 1100 1 1000 no overflow
  since the sign bit of the result is the same as
  the sign bits of the two numbers

25
Excess Notation

• Another binary representation is Excess notation
• Here, there is no special bit for the sign
• Instead, each number is one greater than the
  previous number with the first number in the
  sequence having the value 0
• For instance, excess eight (or 3-bit excess
  notation) has 8 0000 and 7 1111
• See figures 1.22 and 1.23 for examples of Excess
  notations for 3 bits and for 4 bits
• Excess notation is not commonly used for numbers
  themselves but we will see that it is useful to
  use excess notation when representing the
  exponent portion of a floating point number

26
Binary Addition

• Earlier, we examined the Binary Adder
• There, we saw that a sum of two bits has four
  possibilities
• 001, 011, 101, 110 with a carry of 1
• Binary addition is the same process as in decimal
  addition except that we must carry an 1 into the
  next addition (see section 1.5)
• 10011110 01010101
  11100011

27
Fractions and Reals

• We saw earlier that we can use the normal binary
  notation for fractional components
• 1100.1001 12.5625 (8 4 1/2 1/16)
• However, it becomes difficult adding fractions
  together when their decimal points are not
  aligned
• 1100.1001 1.1100011
• Also, we are not used to dealing with fractions
  in many cases
• like dollars and cents
• So, we will use floating point numbers when
  dealing with real numbers and store them using
  scientific notation
• floating point signifies that the decimal point
  is movable (it floats)

28
Scientific Notation

• 38.2839 1 .382839 102
• 1 sign
• we will represent this as (-1)0 or (-1)1 , that
  is, a 0 for even, a 1 for odd
• .382839 mantissa
• Decimal point shifted all the way to the left
• 2 exponent
• How many decimal places we shifted the decimal
  point
• Floating point numbers are represented as three
  values
• sign, mantissa, exponent
• The radix (in the above example is 10) is implied
• The mantissa is normalized so that the decimal
  point precedes the first digit, and then is
  removed
• The sign bit will be a 0 for positive, 1 for
  negative

29
8-bit Floating Point Numbers

• We will use 1 byte for a floating point number
• 1st bit is sign bit
• 2nd-4th bits are exponent in excess 3-bit
  notation (refer to figure 1.23) with an implied
  radix of 2
• 5th-8th bits are normalized mantissa
• Example 01101011
• sign is 0, so positive
• exponent is 110 in excess 3-bit is 2
• mantissa is 1011
• 01101011 1 .1011 22 10.11 2 ¾ 2.75

• Convert -6.5 to binary
• Sign bit is 1
• Mantissa is 6.5 110.1
• To normalize the mantissa
• Change 110.1 to .1101
• By shifting the decimal point three places to the
  left
• This gives an exponent of 23 or a binary exponent
  of 011
• In Excess 3-bit notation, 3 is 111
• So we have a sign bit of 1, an exponent of 111,
  and a mantissa of 1101 or a floating point number
  of 11111101

30
Floating Point Errors

• In our 1 byte example, we cant store much in the
  range of numbers
• between approximately 1/32 and 127
• Consider 2 5/8 which is 10.101
• After normalizing, we have a mantissa of .1010
• we lost a bit off the mantissa
• an exponent of of 110
• giving us 01101010
• If we convert back, we get 10.10 or 2.5
• we have lost 1/8 off of our value!
• This is a round-off or truncation error caused by
  lack of precision

• Try another
• 2 1/2 1/8 1/8
• 2 1/2 01101010
• 1/8 00101000 (1/8 .0010 gt .10002-2)
• If we add 2 1/2 1/8 we get 2 5/8, or 10.101
• But in our floating point notation, we lose the
  last bit so that 01101010 00101000 011010101
• 2 1/2 1/8 2 1/2!
• We add our current sum of 2 1/2 to the final 1/8
  and again we get 2 1/2
• If we add 1/8 1/8 1/4 (00111000)
• Followed by 1/4 2 1/2 01101010 2 5/8

31
Representing Images

• Two common approaches
• Bit maps
• each bit represents a pixel of the picture, a 0
  is black and 1 is white (or vice versa)
• for a color image, we can represent each pixel as
  a code that stands for its color, or we could
  represent the color using a percentage of red,
  green and blue (3 bytes, 1 byte per color)
• Bit maps can be very large and cannot be zoomed
  in on
• Vector
• represent the image as a sequence of lines and
  curves
• Vector graphics may not be as realistic but
  usually require much less memory and can be
  zoomed in on

32
Data Compression

• Used to reduce the size of files
• primarily for image and sound files for storage
  and transmission
• Techniques revolve around
• run-length encoding
• relative encoding
• used in music and video compression
• frequency-dependent encoding
• Huffman codes give shorter codes (fewer bits) to
  letters that occur more commonly (e, t, a, i)
• Lempel-Ziv encoding

• LZ-77 Find repetition in the data and store the
  repetition instead of the actual data
• Ex abac (3, 2, d) (5, 4, e)
• after abac
• count back 3 spaces and repeat the next two
  characters followed by a d
• then count back 5 spaces, repeat the next 4
  characters followed by an e
• gives the string abacbadacbae
• See further examples on pages 61-62

33
Image Compression

• Bit maps tend to create enormous files,
  especially color bit maps
• 3 bytes per pixel, each byte represents the
  degree of red, blue or green in the image
• Special purpose compression formats exist to
  reduce the size of bitmaps
• GIF (Graphic Interchange Format)
• reduce of colors by having a palette and then
  encode the palette number in 1 byte, reducing bit
  maps to 1/3 their original size
• JPEG (Joint Photographic Experts Group) -- used
  for photo quality images
• lossless mode stores changes between adjacent
  pixels
• lossy mode blurs the image by combining 2x2
  pixels into 2 colors and a brightness quality
  reducing the image by half or more

34
Communication Errors

• There is always a chance that information can be
  corrupted during transmission
• over MODEM or LAN lines
• between memory and CPU or I/O/storage device
• Parity bit
• added to every byte to determine error
• parity bit is 1 if number of 1 bits in the byte
  is odd (or even)
• every byte parity bit should have an even (or
  odd) of 1 bits or else an error as arisen
• Notice that the parity bit can detect an error
  but not determine what bit was accidentally
  flipped

35
Error-Correcting Codes

• Another approach is to use a code that permits
  error detection and correction
• Hamming Distance Codes allow this
• In these codes, there is a three bit difference
  between each code so that an error in 1 bit can
  identify the correct value by finding its nearest
  code
• A code with five bit differences between each
  code permits up to 2 errors per transmission with
  the ability to correct
• See figures 1.28 (3 bit) and 1.29 (5 bit)
• Notice that the 5 bit code gets around a problem
  that the 3 bit and parity bit can not solve -- if
  there is more than 1 error in a given byte

36
Hexadecimal and other notations

• Binary notation is awkward
• information in this notation consists of long
  strings of 0s and 1s which are hard to
  understand
• Hexadecimal notation is often used
• Hex is base 16 where 4 bits are combined together
  to form a single Hex digit
• Every hex digit is really a number between 0 and
  15
• In order to permit single digits for 10-15,
  letters are used (A-F)
• See figure 1.6 p. 25 for a Hex-binary conversion
  table
• Other notations are also available, Octal (base
  8) is sometimes used, and of course we all use
  decimal (base 10) notation every day