COMP1105

1
COMP1105

• history
• computer organization,
• hardware and software
• programming languages
• including C!
• computer memory
• number systems
• data representation

• 1. Introduction to computers

2
Fundamentals

• A computer is a device that can input and store
  a set of instructions (program) designed to
  perform a specific task, input and store (data),
  process the stored data according to the
  instructions, and produce output to be relayed to
  its user.
• Computer Systems Properties

• Purpose - Special, General
• Mode - Batch processing, multiprogramming,
  time-sharing, personal, distributed, client
  server
• Type - micro, mini, mainframe, super
• Hardware - memory, CPU, I/O
• Software - Operating system, system software,
  applications,

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Programming languages

• A programming language is an artificial and
  formal language that has a limited set of
  vocabulary consisting of a set of instructions
  and a set of precise grammar rules
• Special purpose programming languages
  structured query language (SQL)
• General programming languages
• Machine language
• Assembly language
• High-level languages

4
Some Programs

• Machine 0000000 1101001 0010011
  0001010 1111011 1010100 1010010
  1011101 0000100 1110111 1110111
  1010101 0001001 0011001 1111111 1010000
• Assembly short hand for machine language
• High-Level Language
• sum firstValue secondValue

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High-level languages
1950 1960 1970 1980 1990
Fortran
Lisp
Algol-60
Cobol
Simula
PL/1
Algol-68
Pascal
Prolog
C
ML
Smalltalk
Ada
Miranda
Object- Oriented languages
Functional languages
Imperative and concurrent languages
Logic languages

• Dates and ancestry of major programming
  languages, Watt 1990

6
Compilation

• Interpretation Compilation

Source program
source program
Compiler
lexical analyser
Target program
input
output
syntax analyser
semantic analyser
efficient, multiple phases
error handler
symbol-table manager
intermediate code generator
Source program
output
Interpreter
code optimiser
input
slower, single phase
code generator
target program
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The C Environment

• C is a compiled language

C Source Program
Your Editor
C Object File
Preprocessed C Source Program
Executable File
Linker
C Compiler
Preprocessor
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Memory

• is where programs and data are stored
• it can be regarded as a sequence of cells
• frequently referred to as RAM (Random Access
  Memory).
• Other types of memory
• ROM (Read Only Memory)
• DRAM (Dynamic RAM)
• SRAM (Static RAM)
• PROM
• EPROM
• Cache memory

• Mass storage -Floppy disks, hard disks, optical
  disks, flash disks, tapes
• Floppy capacity 1.44 Mb (equivalent to 350 A4
  text pages)
• CD-ROM 600 MB (150,000 A4 text pages)
• DVD-ROM 8.4 Gb (2,000,000 A4 text pages)

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Bits bytes

• Bit (Binary digIT) smallest unit
• Kilobit 1,024 bits or 1000 bits
• Megabit 1,024 kilobits or 1,000,000 bits
• Byte (Binary Term) 8 bits
• Kilobyte 210 1,024 bytes or 1000 bytes
• Megabyte 220 1,048,576 bytes
• Gigabyte 230 1,073,741,824 bytes
• Terabyte 240 1,099,511,627,776 bytes (1
  trillion)
• Petabyte 250 1,125,899,906,842,624 bytes or
  1,024 terabytes
• Exabyte 260 1,152,921,504,606,846,976 bytes or
  1,024 petabytes
• Zettabyte 270 1,024 exabytes
• Yottabyte 280 1,024 zettabytes
• Data transfer is measured in Bps, Kbps, Mbps,
  Gbps,

10
Computer memory - Addresses
Memory
0
1
2

• Each memory location has a unique address
• A memory address is a sequential number starting
  at 0
• A bit (binary digit) is a 1 or 0 representing
  an on or off
  state of electricity
• 8 bits represent a byte (character)

32 megabytes
Least significant or Low-order bit
Most significant or High-order bit
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Bits Bytes The Metric System

• When used to describe data transfer rates, bits
  and bytes are calculated as
• 1 MB 1,000,000 bits/bytes
• 1 kb 1,000 bits/bytes
• 1 bit/byte
• Their exact value is as follow
• 1 byte 8 bits
• 1 kilobyte (K / KB) 210 bytes 1,024 bytes
• 1 megabyte (M / MB) 220 bytes 1,048,576
  bytes
• 1 gigabyte (G / GB) 230 bytes 1,073,741,824
  bytes
• 1 terabyte (T / TB) 240 bytes
  1,099,511,627,776 bytes
• 1 petabyte (P / PB) 250 bytes
  1,125,899,906,842,624 bytes
• 1 exabyte (E / EB) 260 bytes
  1,152,921,504,606,846,976 bytes

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Base Systems
13
Number Systems
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Positional property of numbering system

• Each position in which a digit is written has a
  different positional or weighted value

15
Conversion Binary to Decimal

• multiply each digit by its weighted position
• add weighted values together
• Example 1 (Whole Binary) 1100 10102
• 127 1 26 0 25 0 24 1 23 0 22
  1 21 0 20
• 128 64 0 0 8 0 2 0 20210
• Example 2 (Decimal Binary) 0.10112
• 1 2-1 0 2-2 1 2-3 1 2-4
• 1 0.5 0 0.25 1 0.125 1 0.0625
  0.687510

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Conversion Decimal to Binary

• Method 1 Repeated Division by 2
• divide decimal number by 2, the remainder is a
  binary digit and the process continues (by
  dividing the quotient by 2) until quotient
  becomes 0
• begin at the least significant digit (right) and
  each new digit is written to more significant
  digit (the left) of the previous digit
• Example 166

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Conversion Decimal to Binary

• Method 2 The subtraction Method
• For this method, start with a weighted position
  value greater that the number.
• If the number is greater than the weighted
  position for the digit, write down a 1 and
  subtract the weighted position value.
• If the number is less than the weighted position
  for the digit, write down a 0 and subtract 0.
• This process is continued until the result is 0.
• Example 166

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Binary, Octal and Hexadecimal

• From binary
• to octal split binary number into groups of 3
  digits and convert each group to corresponding
  octal
• to hexadecimal split binary number into groups
  of 4
• consider 1000110100012
• Octal equivalent 43218
• Hexadecimal equivalent 8D116

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Binary, Octal and Hexadecimal

• To binary
• Reverse the process rewrite these groups as
  their equivalent octal or hexadecimal
• 1000110100012

43218

• 8D116

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Decimal Conversions

• From decimal to basen (n2,8,16)
• Repeated division by n
• Divide number by n,
• First remainder becomes right-most digit in basen
  number
• Divide quotient by n, the new remainder goes to
  the left of the last digit entered
• Repeat steps (1,2 and 3) until quotient0
• From basen to decimal
• Multiply each digit in basen number by its
  positional values (weighted value)

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Fractions

• Repeat steps until either a zero value is
  obtained for the fractional part or the required
  number of significant digits is obtained.
• Example
• Convert 0.6251010 to base2
• 0.625
• x 2
• 1.250 in binary
• x 2 0.1012
• 0.500
• x 2
• 1.000

• decimal fractions to basen
• Multiply the decimal fraction by n and place the
  integral part of the product as a basen digit in
  the result
• The fractional part of the product is now
  multiplied by n.
• The integral part of the new product is placed as
  basen digit to the right of the last digit in the
  result.

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Fractions basen fractions to decimal

• Decimal fractions can be represented as follows
• 278.3210 2 x 102 7 x 101 8 x 100 3 x 10-1
  2 x 10-2
• 200 70 8 0.3 0.02
• 278.3210
• Similarly, binary fraction can be represented as
• 1010.1012 1 x 23 0 x 22 1 x 21 0 x 20
  1 x 2-1 0 x 2-2 1 x 2-3
• 8 0 2 0 0.5 0 0.125
• 10.62510

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Arithmetic Unsigned integers

• The larger the magnitude of the number, the
  greater the number of bits required in the binary
  representation.
• The smallest number that can be represented is 0
• The largest is 2n - 1, where n is the number of
  bits.

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Signed integers sign magnitude
All 3 The leftmost bit is reserved to represent
the sign of the integer. 0 indicates a positive
number and 1 indicates a negative number.

• sign and magnitude
• 30 00011110
• -30 10011110
• The range of integers that can be stored in
  sign-magnitude is
• -2n-1 - 1 to 2n-1 1
• Problem Simple but requires number validation
  before arithmetic.
• ones complement
• twos complement

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Signed integers 1s Complement

• Leftmost bit is initially set to zero.
• Absolute value of number (binary format) occupies
  the remaining bit places
• For a negative number ALL the bits are then
  complemented (i.e. reverse). Note that this will
  make the sign bit 1 as it should be.
• The 1s complement representation of 30 and 30
  are
• 30 00011110
• -30 11100001
• Problem 0 and 0 are represented differently
  even though they are the same algebraically!
  This causes problems when doing tests on
  arithmetic results.
• computers now use a variation of 1s complement
  (called 2s complement) that eliminates the
  problem.

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Signed integers 2s Complement

• Positive numbers are treated as in ones
  complement.
• Negative numbers representation obtained by
  adding 1 to ones complement representation.
• 1. Start with the absolute value in binary
• 2. Complement all the bits
• 3. Add 1 to the result
• The 8-bit twos complement of representation -30
  is
• Start 00011110
• Complement 30 11100001
• Add 1 1
• -30 11100010

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Addition in 2s Complement

• using n bits, the range of
• integers that can be stored
• in twos complement is
• -2n-1 to 2n-1 1
• 4-bits - we can have 16
• different binary patterns
• 00002 ? 11112

• positive integers
• 0101 (5)
• 0010 (2)
• 01112 (7)
• negative integers
• convert integers into 2s complement
• add as normal
• if result is longer than 4 bits, truncate
  leftmost digit
• obtain 2s complement
• add sign bit

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Subtraction in 2s Complement

• add 2s complement of number
• 0001 1000 (24) 1110 1000 (-24)
• 1101 1011 (-37) 1101 1011 (-37)
• 1111 0011 (-13) 11100 0011 carry
  ignored

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Binary Coded Decimal

• uses 4 bits to represent each decimal digit
• Hexadecimals A-F are unused in BCD, example
• A byte can represent 256 numbers using B, whereas
  only 100 numbers (0-99) can be coded in BCD
• BCD calculations
• Perform B arithmetic on numbers and convert to
  BCD
• Example To store 378,
• Obtain binary equivalent of 3, 7, and 8
  respectively.
• 0011 0111 1000

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Overflow Errors

• 4-bit 2s complement range of values is 7 to 0
  to -8
• ? 5 0101
• 5 0101
• 10 1010
• but 1010 is negative, so 2s complement
• 0110 6, add sign -6
• 10 is out of range Overflow
• overflow is detected
• signs of operands are same, and sign of answer
  different
• or, convert to decimal to validate answer
• To solve this Allow more bits!

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Floating points

• Exponents
• Short hand for multiplication (5)(5) 52,
  (5)(5)(5) 53
• Dealing with numbers we prefer "27" rather than
  "33".  But with variables, we need the exponents,
  because we'd rather deal with "x6" than with
  xxxxxx"
• Simplify (x3)(x4)
• (x3)(x4) (xxx)(xxxxx) xxxxx xx
  x7 x(34)
• we cannot simplify (x4)(y3) (x4)(y3) xxxx
  yyy (x4)(y3)
• For very large or very small numbers it is
  simpler to use "scientific notation"
• 124 (1.24)(100)  1.24 102
• 0.000 000 000 043 6 (4.36)(10)-11

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Floating points

• Real numbers are defined as having both an
  integer and a fractional part.
• Real numbers are represented within computers in
  scientific notation.
• i.e. m x 10p
• where m (the mantissa) - between 0 and 1
• and p (the exponent) is an integer

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Floating points Excess notation

• Excess 2n-1 or biased
• n Number of bits available
• A signed integer N is represented by 2n-1 N.
  Each representation is thus 2n-1 excess in the
  value it represents.
• The binary representation of 2n-1 is a 1 followed
  by n-1 zeros.
• Example 8-bit representation of -7210 in excess
  2n-1 system.
• Solution N -72 n 8
• -72 is represented by -72 28-1
• i.e. -72 128 5610 00111000
• Hence -7210 00111000 in biased form

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Floating points

• 5.7510 101.112 how 5.75 or 143.5 represented?
• convert decimal to Binary
• write binary in normalized scientific notation
• mantissa base exponent
• normalize means
• move binary point (radix) to the left of the most
  significant digit
• adjust values of exponent so value of number is
  unchanged
• 101.112 is written as
• 101.11 20
• 10.111 21
• 1.0111 22
• .10111 2 3
• store normalised binary f x rp

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Floating points
.10111 2 3
1
1
0
0
0
0
0
0
0
0
1
1
1
0
1
0
Mantissa (10 bits)
sign bit
exponent (6 bits)
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Behind the Scenes How Binary, Hexadecimal and
Memory Addressing relates to C

• Signed integer holds a different range of numbers
  than an unsigned
• Unsigned integers range from 0 to 65535
• Signed integers range from 32768 to 32767
• C storage of characters ASCII Table
• char c 65 // Puts the ASCII letter A in c
• int ci A // Puts the number 65 in ci
• Hexadecimal notation is efficient for describing
  memory locations and values, where is data
  value112 stored?
  1111 1111 1011 0101 ? In Decimal? 65461
• System programming with C
• Better interface with Assembly language programs

89
-3
45
66
23
48
1
112
456
-20
56
FFAE FFAF FFB0 FFB1 FFB2 FFB3 FFB4
FFB5 FFB6 FFB7 FFB8