Computer Fundamentals - 1

Instructor
Mr. S.Christalin Nelson
Computer Fundamentals - I

At a Glance
• Evolution of Computers
• Generation of Computers
• Computer Hardware
• Computer Organization
• Types of Computers
• Number Systems
25-Aug-2017
CSEG1001/1101
Instructor: Mr.S.Christalin Nelson|SoCSE|UPES
2 of 127

Introduction
• Origin of Early Computing
– Used fingers & pebbles (‘Digitus’ & ‘Calculus’ in Latin)
• Definition: Data & Information
• Definition: Computer?
• Application Areas
– Business, Industry, Home, Entertainment, Play, Education,
Training, Arts, Science, Engineering, Mathematics, Medicine
and Health Care, Architecture, Communication, Banking,
Publishing, Transportation, Government, etc.
25-Aug-2017
CSEG1001/1101
3 of 127

Evolution of Computers (1/34)
• Abacus
– Sliding beads arranged on rack
• Napier Bones (1617)
– John Napier (1550-1617)
– Logarithms that uses
Multiplication & Addition
25-Aug-2017
CSEG1001/1101
5 of 127

• Multiplication using Napier’s Bones
25-Aug-2017
CSEG1001/1101
6 of 127

• Slide Rule (1632)
– Nasa Engineers
– Multiplication and Division, roots, logarithms, trigonometry
25-Aug-2017
CSEG1001/1101
7 of 127

• Pascaline (1642) – (1/2)
– Blaise Pascal (1623-1662), French mathematician
– Built to help his father, Etienne Pascal, a tax collector, with the
tedious activity of adding & subtracting large sequences of
numbers
– Before 1886 – Calculators without keyboards were based on
Pascaline
– 5/6/8 notched dials (add sums 5/6/8 digits) moved internal
wheels
25-Aug-2017
CSEG1001/1101
8 of 127

• Pascaline (1642) – (2/2)
– Disadvantages
• Costly
• Unreliable
25-Aug-2017
CSEG1001/1101
9 of 127

• Stepped Reckoner (1694)
– Gottfried Wilhelm Von Leibniz (1646-1716) – German
mathematician
– Based on Pascal‘s design
– Basic arithmetic op.
• Addition, subtraction, multiplication, division & square root
– Disadvantages
• Lacked mechanical precision
• Not reliable
25-Aug-2017
CSEG1001/1101
10 of 127

• Difference Engine (1822)
– Charles Babbage (1791-1871) – English Mathematician
– Steam powered machine (size of locomotive)
– Had stored program that performs calculations and prints
result automatically
– Tabulate logarithms &trigonometric functions by evaluating
finite differences to create approximating polynomials
– Disadvantage
• Not fully functional
25-Aug-2017
CSEG1001/1101
11 of 127

• Difference Engine of Charles Babbage
25-Aug-2017
CSEG1001/1101
12 of 127

• Analytical Engine (1833)
– Charles Babbage (1791-1871) – English Mathematician
– Input (Operating Instructions) – perforated cards (later
punched cards - Joseph-Marie Jacquard’s loom)
– Memory (1000 nos. , upto 50 decimal digits long)
– Control unit (process instructions in any sequence)
– Output - a printer, a curve plotter and a bell
– The machine would also be able to punch numbers onto cards
to be read in later
– Note: Was not constructed but it outlined basic elements of
modern computers
25-Aug-2017
CSEG1001/1101
13 of 127

• Analytical Engine (1833)
25-Aug-2017
CSEG1001/1101
14 of 127

• Jacquard’s Loom & Punched Cards
25-Aug-2017
CSEG1001/1101
15 of 127

• Tabulator (1889)
– Herman Hollerith
– Applied punched cards - Joseph-Marie Jacquard’s loom
• Used to store data – fed into machine – compiled results
mechanically
Memory Tape
25-Aug-2017
CSEG1001/1101
16 of 127

• Herman Hollerith’s Tabulator
25-Aug-2017
CSEG1001/1101
17 of 127

• Mark I (1944)
– Harvard Aiken & IBM
– Electronics machine – used relays, electromagnetic
components
25-Aug-2017
CSEG1001/1101
18 of 127

• Manchester Mark I
25-Aug-2017
CSEG1001/1101
19 of 127

• ENIAC
– Full Name
• Electronic Numerical Integrator and Calculator
– Birth: 1946
– Birth Place
• Moore School of Engg., Univ. of Pennsylvannia
– Parents
• John Eckert & John Mauchly
– Life: 10 years
– Weight: 27000kg
– Area: 1800sq.m
– Power Consumption: 150kW
– Cost: $6Lakh
25-Aug-2017
CSEG1001/1101
20 of 127

• ENIAC at Moore School
25-Aug-2017
CSEG1001/1101
21 of 127

• ENIAC (1946)
– Design
• 17500 Electronic Vacuum Tubes, 1500 Relays, 7200 diodes, 70000
Resistors, 10000 capacitors
• Input: IBM Card Reader, Output: IBM Card Punch
– Offline Printed Output: IBM Accounting machine IBM405
• Data Memory: 20 Accumulators
– Each Accumulator stores 10-digit decimal no. (Each digit: Ring of 10
Vacuum tubes)
– Function
• Compute ballistic trajectories
• Number System & Arithmetic: Decimal
– Performed 500 Additions/Subtractions per sec
– Disadvantage: Wired for specific computations
• Modification/Replacement of programs done manually25-Aug-2017
CSEG1001/1101
22 of 127

• ENIAC
25-Aug-2017
CSEG1001/1101
23 of 127

• EDVAC
– Full Name
• Electronic Discrete Variable Automatic Computer
– Birth: 1949
– Birth Place
• Moore School of Engg., Univ. of Pennsylvannia
– Parents
• John Eckert & John Mauchly, John Von Neumann
– Weight: 7850kg
– Area: 50sq.m
– Power Consumption: 56kW
– Cost: $5Lakhs
25-Aug-2017
CSEG1001/1101
24 of 127

• EDVAC Mainframe Computer
25-Aug-2017
CSEG1001/1101
25 of 127

• EDVAC
– Design
• 6000 Vacuum tubes, 12000 Diodes
• Number System & Arithmetic: Binary
– Features
• First Electronic computer which adopted stored program concept
of John Von Neumann
• Conditional control transfer (stop and resume later)
25-Aug-2017
CSEG1001/1101
26 of 127

• EDSAC (1949)
– Electronic Delay Storage Automatic Calculator
– Team headed by Maurice Wilkes, Cambridge Univ.
– Adopted stored program concept of John Von Neumann
• Vacuum tubes - logic, Mercury delay lines - memory
25-Aug-2017
CSEG1001/1101
27 of 127

IBM 701, IBM 702, IBM AN/FSQ-7 whirlwind, IBM 704
25-Aug-2017
CSEG1001/1101
28 of 127

IBM 1401, IBM 709
25-Aug-2017
CSEG1001/1101
29 of 127

IBM 7030, System/360, Digital VAX-11/780
25-Aug-2017
CSEG1001/1101
30 of 127

IBM 3083, Mainframe Computer Server
25-Aug-2017
CSEG1001/1101
31 of 127

• UNIVAC (1951)
– Universal Automatic Computer
– Beginning of Computer Era
• 1960s
– LARC machine
• Access time : < 1 microsec.
• Capacity: 10,00,00,000 words
– Other developments
• Computer Manufacturers offered range of capabilities & prices
• Accessories: Card feeders, page printers, CRT display
25-Aug-2017
CSEG1001/1101
32 of 127

• UNIVAC
25-Aug-2017
CSEG1001/1101
33 of 127

• 1970s
– Range of applications vs. cheaper computer systems
– Business organizations used computers in offices
– Transistors – Vacuum depositions
– IC chip – housed computer assemblies
• Development of Microprocessors & Processors on single IC chip
25-Aug-2017
CSEG1001/1101
34 of 127

Apple 1 (1976)
25-Aug-2017
CSEG1001/1101
35 of 127

• 1980s
– VLSI - Chip housed 100s of 1000s of transistors
– Introduction of PCs
• Microprocessors with ROM performed no. of functions
– Late 1980s – PC run by microprocessors
• Handled 32bits data at a time
• Process 4,000,000 instructions per sec.
25-Aug-2017
CSEG1001/1101
36 of 127

• 1990s
– PC – part of everyday life (homes, offices, schools, etc.)
– Microprocessors shrunk in size with increasing processing
power
– Applications
• Email, Computer Networking, electronic publishing, etc.
25-Aug-2017
CSEG1001/1101
37 of 127

25-Aug-2017
CSEG1001/1101
IBM PC (1990)
38 of 127

Computer Generations (1/10)
• First Generation (1940 – 56): Vacuum Tubes
– Specification
• Vacuum tubes -> circuitry
• Magnetic drums -> memory
• Input ->punched cards and paper tape
• Output ->printouts
– Binary Coded Language (0s & 1s)
• Perform operations, Solve one problem at a time
– Examples: ENIAC, EDVAC, UNIVAC
– Disadvantage
• Difficult to program (instructions should be recompiled for other
machines), lack of versatility & speed
• Expensive, Huge conception of electricity, Big & Clumsy
25-Aug-2017
CSEG1001/1101
40 of 127

25-Aug-2017
CSEG1001/1101
41 of 127

• Second Generation (1956 – 63): Transistors
– Transistor
• Used to relay and switch electronic signals
– Assembly language
– Specification
• Punched cards for input
• Printouts for output
• Transistor for circuits
• Magnetic core technology for memory
– Computers smaller, faster, cheaper, more energy-efficient
25-Aug-2017
CSEG1001/1101
42 of 127

25-Aug-2017
CSEG1001/1101
43 of 127

• Third Generation (1964 – Early 1970s): IC
– Integrated Circuits
• Transistors were miniaturized and placed on silicon chips called
semiconductors
– High Level Language
– Specifications
• Keyboard as input
• Monitor as output
• Operating System
– Central program that controls the devices
– Advantages
• Speed, Efficiency
25-Aug-2017
CSEG1001/1101
44 of 127

25-Aug-2017
CSEG1001/1101
45 of 127

• Fourth Generation (Early 1970s – Till Date): Microprocessors
– Data Communication
– Microprocessors
• 1000s of ICs were built onto a single silicon chip
• Properties
– Instruction set, Bandwidth, Clock Speed
– Example
• Intel 4004 chip, 1984 Apple introduced the Macintosh
– Specification
• Microprocessor, Mouse and other handheld devices, CPU and
ALU, RAID – Redundant array of Independent Disk
25-Aug-2017
CSEG1001/1101
46 of 127

25-Aug-2017
CSEG1001/1101
47 of 127

• Fifth Generation (Present and Beyond): Artificial Intelligence
– Artificial Intelligence
• Game Playing
• Expert System
– Robotics
– Voice Recognition
– Example
• No fully AI computers
• 1997, an IBM super-computer called Deep Blue defeated world
chess champion Gary Kasparov in a chess
25-Aug-2017
CSEG1001/1101
48 of 127

• Moore’s Law
– This law states that processor speeds, or overall processing
power for computers will double every two years
– To break down the law even further, it specifically stated that
the number of transistors on an affordable CPU would double
every two years
• LSI, VLSI,….
25-Aug-2017
CSEG1001/1101
49 of 127

Case Preparation
25-Aug-2017
CSEG1001/1101
51 of 127

Inside the Cabinet
25-Aug-2017
CSEG1001/1101
52 of 127

Mother Board
A. USB port
B. PS/2 port
C. Parallel port
D. Serial port
E. ATX power supply
F. AGP
G. PCI slot
H. CPU slot
I. Memory slot
J. IDE Controller
K. IDE Floppy Control
L. IDE Controller
M. Clock Battery
N. Audio Modem Riser
Slot
25-Aug-2017
CSEG1001/1101
53 of 127

CPU Installation
• Socket Type
• Slot Type
25-Aug-2017
CSEG1001/1101
54 of 127

Heat Sink / Cooling Fan
25-Aug-2017
CSEG1001/1101
55 of 127

RAM
25-Aug-2017
CSEG1001/1101
56 of 127

Hard Drive Installation
25-Aug-2017
CSEG1001/1101
57 of 127

25-Aug-2017
CSEG1001/1101
RAM
Hard Disk
System Fan
CPU
Bluetooth
Board
Battery
Slot
Motherboard
59 of 127

25-Aug-2017
CSEG1001/1101
• RAM
60 of 127

25-Aug-2017
CSEG1001/1101
• Hard Disk
61 of 127

25-Aug-2017
CSEG1001/1101
CMOS
Bluetooth Board
Keyboard plate
62 of 127

Major Components of Computer
Control Unit
Memory Unit
Arithmetic &
Logical Unit (ALU)
Secondary Storage
Input Unit Output Unit
Control Flow
Data Flow
• Block Diagram of Computer
25-Aug-2017
CSEG1001/1101
64 of 127

Memory Organization
• Memory Hierarchy
– Processor registers
• Fastest possible access (≈ 1 CPU cycle), hundreds of bytes in size
– Level 1 (L1) cache
• Often accessed in just a few cycles, usually tens of kilobytes (kB)
• Higher latency than L1 by 2× to 10×, often 512kB or more
• Higher latency than L2, often 2048kB or more
– Main memory
• May take hundreds of cycles, but can be multiple GB
– Disk storage
• Millions of cycles latency if not cached, but very large
– Tertiary storage – several seconds latency, can be huge25-Aug-2017
CSEG1001/1101
65 of 127

Computer Types
• Micro-Computers
• Mini-Computers
• Mainframes
• Super-Computers
• Servers
25-Aug-2017
CSEG1001/1101
67 of 127

Microcomputer (1/3)
• Synonymous with personal computer, it has Microprocessor
as CPU on a microchip, a memory system (typically ROM and
RAM), a bus system and I/O ports, typically housed in a
motherboard.
• Microcomputers became popular in the 1970s and 80s with
the advent of increasingly powerful microprocessors.
• They are designed to be used by individuals, in the form of
– Personal Computers
– Workstations
– Notebook computers
25-Aug-2017
CSEG1001/1101
68 of 127

Microcomputer (2/3)
• Personal computer (PC)
– It is a small, relatively inexpensive computer designed for an
individual user.
– PCs can be used for word processing, accounting, desktop
publishing, running spreadsheet and database management
applications, games, etc.
• Notebook Computers
– It is extremely lightweight and portable than a PC.
– Use display screens of different technology compared with PC.
– In terms of computing power, modern notebook computers
are nearly equivalent to personal computers.
– Notebook computers come with battery packs.
25-Aug-2017
CSEG1001/1101
69 of 127

Microcomputer (3/3)
• Workstations
– Workstations are single-user computers typically networked
although they can also be used as stand-alone systems.
– Use moderate amount of computing power and relatively high
quality graphics capabilities.
– Workstations generally come with a large, high-resolution
graphics screen, at least 64 MB of RAM, built-in network
support, GUI and mass storage device such as a disk drive.
Diskless workstation also exist.
– It is used for engineering applications (CAD/CAM), desktop
publishing, software development, etc.
– In terms of computing power, workstations lie between PC and
minicomputers.
25-Aug-2017
CSEG1001/1101
70 of 127

Minicomputer
• A minicomputer is a multiprocessing mid-sized computer
capable of supporting from 4 to about 200 users
simultaneously.
• In size and power, minicomputers lie between workstations
and mainframes.
25-Aug-2017
CSEG1001/1101
71 of 127

Mainframe
• A very large and expensive computer capable of supporting
hundreds, or even thousands, of users simultaneously.
• In the hierarchy that starts with a simple microprocessor (in
watch, etc.) at the bottom and moves to supercomputers at
the top, mainframes are just below supercomputers.
• Vs. Supercomputer
– Mainframes are more powerful than supercomputers as they
support more simultaneous programs. But supercomputers
can execute a single program faster than a mainframe.
25-Aug-2017
CSEG1001/1101
72 of 127

Supercomputer
• Supercomputers are the fastest type of computers, very
expensive and are employed for specialized applications that
require immense amounts of mathematical calculations.
• It is used for weather forecasting, animated graphics, fluid
dynamic calculations, nuclear energy research, and
petroleum exploration.
• Vs. Mainframe
– A supercomputer channels all its power into executing a few
programs as fast as possible, whereas a mainframe uses its
power to execute many programs concurrently.
25-Aug-2017
CSEG1001/1101
73 of 127

Servers
• It is a high-end dedicated computer on a network that
manages network resources.
• There are many different types of servers.
– File server: a computer and storage device dedicated to storing
files. Any user on the network can store files on the server.
– Web server: a computer that delivers Web pages to clients.
– Proxy server: It sits between a client application, such as a
Web browser, and a real server. It intercepts all requests to the
real server to see if it can fulfill the requests itself. If not, it
forwards the request to the real server.
• Purpose of a Proxy Server: improve performance, filter requests
– Network server: a computer that manages network traffic.
– Database server: a computer that processes database queries.
– Print server: a computer that manages one or more printers.25-Aug-2017
CSEG1001/1101
74 of 127

Common Number Systems
System Base Symbols
Used by
humans?
Used in
computers?
Decimal 10 0, 1, … 9 Yes No
Binary 2 0, 1 No Yes
Octal 8 0, 1, … 7 No No
Hexa-decimal 16 0, 1, … 9, A, B, … F No No
25-Aug-2017
CSEG1001/1101
76 of 127

Quantities / Counting
25-Aug-2017
CSEG1001/1101
Dec Bin Oct Hex
0 0 0 0
1 1 1 1
2 10 2 2
3 11 3 3
4 100 4 4
5 101 5 5
6 110 6 6
7 111 7 7
Dec Bin Oct Hex
8 1000 10 8
9 1001 11 9
10 1010 12 A
11 1011 13 B
12 1100 14 C
13 1101 15 D
14 1110 16 E
15 1111 17 F
Dec Bin Oct Hex
16 10000 20 10
17 10001 21 11
18 10010 22 12
19 10011 23 13
20 10100 24 14
21 10101 25 15
22 10110 26 16
23 10111 27 17
………..Etc.
77 of 127

Number System Conversion Among Bases
• The possibilities:
Hexadecimal
Decimal Octal
Binary
25-Aug-2017
CSEG1001/1101
78 of 127

Quick Example
25-Aug-2017
CSEG1001/1101
2510 = 110012 = 318 = 1916
Base
79 of 127

Binary to Decimal (1/2)
• Procedure
– Multiply each bit by 2n, where n is the position of the bit
starting from 0 on the right
– Add the results
25-Aug-2017
Hexadecimal
Decimal Octal
Binary
CSEG1001/1101
80 of 127

Binary to Decimal (2/2)
• Example: Convert (101011)2 to Decimal
25-Aug-2017
CSEG1001/1101
1010112 => 1 x 20 = 1
1 x 21 = 2
0 x 22 = 0
1 x 23 = 8
0 x 24 = 0
1 x 25 = 32
4310
Bit “0”
81 of 127

Octal to Decimal (1/2)
• Procedure
– Multiply each digit by 8n, where n is the position of the digit,
– Add the results
25-Aug-2017
Hexadecimal
Decimal Octal
Binary
CSEG1001/1101
82 of 127

Octal to Decimal (2/2)
• Example: Convert (724)8 to Decimal
25-Aug-2017
CSEG1001/1101
7248 => 4 x 80 = 4
2 x 81 = 16
7 x 82 = 448
46810
83 of 127

Hexadecimal to Decimal (1/2)
• Procedure
– Multiply each digit by 16n, where n is the position of the bit,
– Add the results
25-Aug-2017
Hexadecimal
Decimal Octal
Binary
CSEG1001/1101
84 of 127

Hexadecimal to Decimal (2/2)
• Example: Convert (ABC)16 to Decimal
25-Aug-2017
CSEG1001/1101
ABC16 => C x 160 = 12 x 1 = 12
B x 161 = 11 x 16 = 176
A x 162 = 10 x 256 = 2560
274810
85 of 127

Decimal to Binary (1/2)
• Procedure
– Divide number/quotient by 2 and keep track of the remainder
until quotient is 0
– Construct the result with Remainder
• First remainder is first digit from Right (LSB, least-significant bit)
• Second remainder is second digit, etc.
25-Aug-2017
Hexadecimal
Decimal Octal
Binary
CSEG1001/1101
86 of 127

Decimal to Binary (2/2)
• Example: Convert (125)10 to Binary
25-Aug-2017
CSEG1001/1101
12510 = ?2
2 125
62 12
31 02
15 12
7 12
3 1
2
0 1
12510 = 011111012
2
1 1
87 of 127

Octal to Binary (1/2)
• Procedure
– Convert each octal digit to a 3-bit equivalent binary
representation
25-Aug-2017
Hexadecimal
Decimal Octal
Binary
CSEG1001/1101
88 of 127

Octal to Binary (2/2)
• Example: Convert (705)8 to Binary
25-Aug-2017
CSEG1001/1101
7 0 5
111 000 101
7058 = 1110001012
7058 = ?2
89 of 127

Hexadecimal to Binary (1/2)
• Procedure
– Convert each hexadecimal digit to a 4-bit equivalent binary
representation
25-Aug-2017
Hexadecimal
Decimal Octal
Binary
CSEG1001/1101
90 of 127

Hexadecimal to Binary (2/2)
• Example: Convert (10AF)16 to Binary
25-Aug-2017
CSEG1001/1101
10AF16 = ?2
1 0 A F
0001 0000 1010 1111
10AF16 = 00010000101011112
91 of 127

Binary to Octal (1/2)
• Procedure
– Group bits in threes, starting from right
– Convert to octal digits
25-Aug-2017
Hexadecimal
Decimal Octal
Binary
CSEG1001/1101
92 of 127

Binary to Octal (2/2)
• Example: Convert (10110 10111)2 to Octal
25-Aug-2017
CSEG1001/1101
10110 101112 = ?8
1 011 010 111
1 3 2 7
10110101112 = 13278
93 of 127

Decimal to Octal (1/2)
• Procedure
until quotient is 0
• First remainder is first digit from Right
25-Aug-2017
Hexadecimal
Decimal Octal
Binary
CSEG1001/1101
94 of 127

Decimal to Octal (2/2)
• Example: Convert (1234)10 to Octal
25-Aug-2017
CSEG1001/1101
123410 = ?8
8 1234
154 28
19 28
2 38
0 2
123410 = 23228
95 of 127

Hexadecimal to Octal (1/2)
• Procedure
– Convert Hexadecimal to Binary
– Group 3 digits from right and represent it with an Octal
number
25-Aug-2017
Hexadecimal
Decimal Octal
Binary
CSEG1001/1101
96 of 127

Hexadecimal to Octal (2/2)
• Example: Convert (1F0C)16 to Octal
25-Aug-2017
CSEG1001/1101
1F0C16 = ?8
1 F 0 C
0001 1111 0000 1100
1 7 4 1 4
1F0C16 = 174148
97 of 127

Decimal to Hexadecimal (1/2)
• Procedure
until quotient is 0
• First remainder is first digit from Right
25-Aug-2017
Hexadecimal
Decimal Octal
Binary
CSEG1001/1101
98 of 127

Decimal to Hexadecimal (2/2)
• Example: Convert (1234)10 to Hexadecimal
25-Aug-2017
CSEG1001/1101
123410 = ?16
123410 = 4D216
16 1234
77 216
4 13 = D16
0 4
99 of 127

Binary to Hexadecimal (1/2)
• Procedure
– Group bits in fours, starting on right
– Convert to hexadecimal digits
25-Aug-2017
Hexadecimal
Decimal Octal
Binary
CSEG1001/1101
100 of 127

Binary to Hexadecimal (2/2)
• Example: Convert (10101 11011)2 to Hexadecimal
25-Aug-2017
CSEG1001/1101
10101110112 = ?16
10 1011 1011
2 B B
10101110112 = 2BB16
101 of 127

Octal to Hexadecimal (1/2)
• Procedure
– Convert Octal to Binary
– Group 4 digits from right and represent it with an Hexadecimal
number
25-Aug-2017
Hexadecimal
Decimal Octal
Binary
CSEG1001/1101
102 of 127

Octal to Hexadecimal (2/2)
• Example: Convert (1076)8 to Hexadecimal
25-Aug-2017
CSEG1001/1101
10768 = ?16
1 0 7 6
001 000 111 110
2 3 E
10768 = 23E16
103 of 127

Activity – I
• Convert the following into other Number System values
25-Aug-2017
CSEG1001/1101
Don’t use a calculator!
Decimal Binary Octal Hexa-decimal
33 ? ? ?
? 1110101 ? ?
? ? 703 ?
? ? ? 1AF
104 of 127

Activity – I (contd.)
25-Aug-2017
CSEG1001/1101
33 100001 41 21
117 1110101 165 75
451 111000011 703 1C3
431 110101111 657 1AF
105 of 127

Fractions (1/9)
• Decimal to decimal (just for fun)
3.14 => 4 x 10-2 = 0.04
1 x 10-1 = 0.1
3 x 100 = 3
3.14
25-Aug-2017
CSEG1001/1101
106 of 127

Fractions (2/9)
• Binary to Decimal
10.10112 => 1 x 2-4 = 0.0625
1 x 2-3 = 0.125
0 x 2-2 = 0.0
1 x 2-1 = 0.5
0 x 20 = 0.0
1 x 21 = 2.0
2.6875
25-Aug-2017
CSEG1001/1101
10.10112 = 2.687510
107 of 127

Fractions (3/9)
• Octal to Decimal
21.218 => 1 x 8-2 = 00.016
2 x 8-1 = 00.250
1 x 80 = 01.000
2 x 81 = 16.000
17.266
25-Aug-2017
CSEG1001/1101
21.218 = 17.26610
108 of 127

Fractions (4/9)
• Hexadecimal to Decimal
EF.B116 => 1 x 16-2 = 000.004
B(11) x 16-1 = 000.688
F(15) x 160 = 015.000
E(14) x 161 = 224.000
239.692
25-Aug-2017
CSEG1001/1101
EF.B18 = 239.69210
109 of 127

Fractions (5/9)
• Decimal to Binary
3.1457910
.14579
x 2
0.29158
x 2
0.58316
x 2
1.16632
x 2
0.33264
x 2
0.66528
x 2
1.33056
etc.11.001001...
25-Aug-2017
CSEG1001/1101
3.1457910 = 11.0010012
110 of 127

Fractions (6/9)
• Decimal to Hexadecimal
• Note: Conversion of a fraction from Decimal to another Number system
requires multiplication of its fractional part by the new base
0.062810
0.0628
x 16
1.0048
x 16
0.0768
x 16
1.2288
x 16
3.6608
0.1013...
25-Aug-2017
CSEG1001/1101
0.062810 = 0.101316
111 of 127

Fractions (7/9)
• Binary to Octal
– For a Binary fraction, arrange the bits into groups of 3 starting
at the binary point and move towards the right. Then each
group is replaced by the corresponding octal digit. If the
number of bits is not a multiple of 3, add necessary number of
zeros to the left of MSB.
– Example: 111101.011012
• 111101.011010 = 75.328
• Octal to Binary
– Replace each Octal digit by its 3-bit binary equivalent.
25-Aug-2017
CSEG1001/1101
112 of 127

Fractions (8/9)
• Binary to Hexadecimal
– For a Binary fraction, arrange the bits into groups of 4 starting
at the binary point and move towards the right. Then each
group is replaced by the corresponding hexadecimal digit. If
the number of bits is not a multiple of 4, add necessary
number of zeros to the left of MSB.
– Example: 111101.011012
• 111101.011010 = 3D.6216
• Hexadecimal to Binary
– Replace each Hexadecimal digit by its 4-bit binary equivalent.
25-Aug-2017
CSEG1001/1101
113 of 127

Fractions (9/9)
• Octal to Hexadecimal
– Example: 56.358
• Step-1: (56.35)8 = (101110. 011101)2
• Step-2: (101110. 011101)2 = (00101110. 01110100)2 = (2E.74)16
• Hexadecimal to Octal
– Example: 2E.7416
• Step-1: (2E.74)16 = (00101110. 01110100)2
• Step-2: (000101110. 011101000)2 = (056.350)8 = (56.35)8
25-Aug-2017
CSEG1001/1101
114 of 127

Activity – II
25-Aug-2017
CSEG1001/1101
29.8 ? ? ?
? 101.1101 ? ?
? ? 3.07 ?
? ? ? C.82
115 of 127

Activity – II (contd.)
25-Aug-2017
CSEG1001/1101
29.8 11101.110011… 35.63… 1D.CC…
5.8125 101.1101 5.64 5.D
3.109375 11.000111 3.07 3.1C
12.5078125 1100.10000010 14.404 C.82
116 of 127

Common Powers (1/3)
• Base 10
Power Preface Symbol
10-12 pico p
10-9 nano n
10-6 micro 
10-3 milli m
103 kilo k
106 mega M
109 giga G
1012 tera T
Value
.000000000001
.000000001
.000001
.001
1000
1000000
1000000000
1000000000000
25-Aug-2017
CSEG1001/1101
117 of 127

Common Powers (2/3)
• Base 2
– In computing, particularly w.r.t. memory, the base-2
interpretation generally applies
Power Preface Symbol
210
kilo k
220
mega M
230
Giga G
Value
1024
1048576
1073741824
25-Aug-2017
CSEG1001/1101
118 of 127

Common Powers (3/3)
• Base 2 (Example)
•
• Double click My Computer
Right click on C:
Click on Properties
25-Aug-2017
CSEG1001/1101
/ 230 =
119 of 127

Common Bases
• For common bases, add powers
26  210 = 216 = 65,536
or…
26  210 = 64  210 = 64k
ab  ac = ab+c
25-Aug-2017
CSEG1001/1101
120 of 127

Binary Addition (1/2)
• Two 1-bit values
A B A + B
0 0 0
0 1 1
1 0 1
1 1 10
“two”
25-Aug-2017
CSEG1001/1101
121 of 127

Binary Addition (2/2)
• Two n-bit values
– Add individual bits & Propagate carries
– E.g. Add (10101)2 and (11001)2
10101 21
+ 11001 + 25
101110 46
11
25-Aug-2017
CSEG1001/1101
“carry”
122 of 127

Binary Multiplication (1/3)
• Multiplication of Decimal Numbers
– A view as “Sum of the Partial Products”
35
x 105
175
000
35
3675
25-Aug-2017
CSEG1001/1101
123 of 127

• Binary, two 1-bit values
A B A  B
0 0 0
0 1 0
1 0 0
1 1 1
25-Aug-2017
CSEG1001/1101
124 of 127

• Binary, two n-bit values
– Same as multiplication of two decimal values
– E.g. Multiply (1110)2 and (1011)2
1110
x 1011
1110
1110
0000
1110
10011010
25-Aug-2017
CSEG1001/1101
“partial product”
125 of 127

Peep into the next Module
• Computer Fundamentals – II
– Generation of Programming Languages
– Programming Paradigms
– Structure & Execution Environment of a Basic C Program
– Software Engineering & Problem Solving Methods
– Need of Translators, Linkers, Locaters, Loaders & Editors
25-Aug-2017
CSEG1001/1101
126 of 127

Computer Fundamentals - 1

More Related Content

What's hot (20)

Similar to Computer Fundamentals - 1 (20)

More from Christalin Nelson (20)

Recently uploaded (20)

Computer Fundamentals - 1