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 A machine capable of following instruction to
alter data in a desirable way and to perform at
least some of these operations without human
intervention.
 A computer is a programmable machine that
receives input, stores and manipulates data,
and provides output in a useful format.
 Computer was used as an electronic device that
allows inputting data and having it stored,
processed, or otherwise manipulated quickly
and efficiently.
www.mrblanco.page4.me 2
 The repetitive process of computation
leads to people becoming bored in
computing such as navigational table,
tide charts, and planetary positions for
astronomical almanacs. People were
doing these things everyday and this is
the reason why people invented
computers, that is to aid in numerous
computation required everyday.
www.mrblanco.page4.me 3
 The Abacus
 The first computing aid that were used to help
them in their computation.
www.mrblanco.page4.me 4
 The Napier’s Bone
 An abacus created by John Napier for calculation
of products and quotients of numbers that was
based on Arab mathematics and lattice
multiplication used by Fibonacci writing in the
Liber Abaci.
www.mrblanco.page4.me 5
 The Slide Rule
 Used primarily for multiplication and division,
and also for "scientific" functions such as roots,
logarithms and trigonometry, but is not
normally used for addition or subtraction.
www.mrblanco.page4.me 6
 The Calculating Clock/ Schickard Calculator
 Consisted of a six-digit machine that could add or
subtract.
 Wilhelm Schickard developed it on 1623 in Tübingen,
Württemberg
www.mrblanco.page4.me 7
 The Pascaline
 The first calculator or adding machine to be
produced in any quantity and actually used. It
could only do addition and subtraction, with
numbers being entered by manipulating its dials.
 designed and built by the French mathematician-
philosopher Blaise Pascal between 1642 and 1644
www.mrblanco.page4.me 8
 The Step Reckoner
 The first calculator that could perform all four
arithmetic operations: addition, subtraction,
multiplication and division.
 invented by German mathematician and philosopher
Gottfried Wilhelm Leibniz around 1672 and
completed 1694
www.mrblanco.page4.me 9
 The Difference Engine
 An automatic, mechanical calculator designed to
tabulate polynomial functions.
 By 1822 the English mathematician Charles Babbage
who is considered as Father of the Computer today
was proposing a steam driven calculating machine
the size of a room
www.mrblanco.page4.me 10
 The Hollerith's Tabulating Machine
 the electro-mechanical tabulator.
 On the tabulator's desk to the right is a press-like
device which would bring an array of pins into
contact with a punch card.
www.mrblanco.page4.me 11
 The Mark I
 The first large-scale automatic digital computer
in the USA by Howard H. Aiken, built at IBM
and shipped to Harvard in February 1944.
www.mrblanco.page4.me 12
 The Apple I
 An early personal computer.
 They were designed and hand-built by Steve
Wozniak
www.mrblanco.page4.me 13
 The PDP-12
 A 12 bit machine introduced in 1969.
Applications included applied psychology,
chemistry, patient monitoring, and industrial
testing.
www.mrblanco.page4.me 14
 The IBM Personal Computer
 The original version and progenitor of the IBM
PC compatible hardware platform.
www.mrblanco.page4.me 15
 The Personal Computer
 any general-purpose computer whose size,
capabilities, and original sales price make it
useful for individuals, and which is intended to
be operated directly by an end user, with no
intervening computer operator.
www.mrblanco.page4.me 16
 Netbooks
 A branch of subnotebooks, a rapidly evolving
category of small, lightweight, and inexpensive
laptop computers suited for general computing
and accessing Web-based applications; they are
often marketed as "companion devices", i.e., to
augment a user's other computer access.
www.mrblanco.page4.me 17
 Open
 A task that display a document window.
 Close
 In a program that can be display more than one document
window, to remove a window from the display.
 Copy
 A simple method of reproducing text or other data from a
source to a destination.
 Cut
 To move one file in to another path or location.
www.mrblanco.page4.me 18
 Paste
 Used to join files horizontally (parallel merging) by
outputting lines consisting of the sequentially
corresponding lines of each file specified, separated by tabs,
to the standard output.
 Rename
 To change the name of the file.
 Delete
 To remove the files from the folder or into the desktop.
 Web Browser
 A software application used for retrieving, presenting, and
traversing information resources on the World Wide Web.
www.mrblanco.page4.me 19
 Directory
 A virtual container within a digital file system, in which
groups of computer files and other folders can be kept and
organized.
  Web Page
 A document or resource of information that is suitable for
the World Wide Web and can be accessed through a web
browser and displayed on a computer screen.
 Web Site
 A collection of related web pages, images, videos or other
digital assets that are addressed with a common domain
name or IP address in an Internet Protocol-based network.
www.mrblanco.page4.me 20
 Computer Hardware
 The physical component of computer system
which can be installed an operating system and a
multitude of software to perform the operator’s
desired functions.
 Hardware Components
 Input Devices
Input devices are things we use to put information
INTO a computer.
 Output Devices
Output devices are things we use to get information
OUT of a computer.www.mrblanco.page4.me 21
www.mrblanco.page4.me 22
 Memory
 Refers to devices that are used to store data or
programs on a temporary or permanent basis for
use in an electronic digital computer.
 Microprocessors
 A microprocessor incorporates most or all of the
functions of a computer's central processing unit
(CPU) on a single integrated circuit (IC, or
microchip).
www.mrblanco.page4.me 23
 Computer Software
 The intangible part of the computer system.
 Operating System Software
 A master control program for a computer that manages
the computer’s internal functions and provides you
with a means to control the computer’s operation.
 Software Applications
 Computer software designed to help the user to
perform a singular or multiple related specific tasks.
Such programs are also called software applications,
applications or apps.www.mrblanco.page4.me 24
 Peopleware
 Refer to anything that has to do with the role
of people in the development or use of
computer software and hardware systems,
including such issues as developer
productivity, teamwork, group dynamics, the
psychology of programming, project
management, organizational factors, human
interface design, and human-machine-
interaction.
www.mrblanco.page4.me 25
 Operating system designed and
produced by Microsoft Corporation.
Similar to other operating systems,
Windows makes a computer system
user-friendly by providing a graphical
display and organizing information so
that it can be easily accessed.
www.mrblanco.page4.me 26
 Parts of a Window:
The Title Bar contains the name of the
application or folder. It also contains the
standard Windows 98 control buttons. Drag the
title bar to move a window by holding down
the left mouse button as you drag the window.
Control-Menu Icon allows you to minimize,
maximize, restore, or close a window. Right
click on the Control button to see the drop
down list. Left click on the title bar to close the
drop down menu.
Microsoft Windows
www.mrblanco.page4.me 27
 Parts of a Window:
Menu Bar provides pull down menus to access
Windows 98 commands.
Icons are graphic symbols used to represent
an application or folder.
Control Buttons allow you to minimize,
maximize, restore, or close a window.
Window Border is a frame around a window
that allows you to resize a window. You can
drag a window's border to resize a window.
Microsoft Windows
www.mrblanco.page4.me 28
Ergonomics & Positioning
 The positioning of your body as well as the
physical layout of the work environment
and equipment will significantly impact
your overall efficiency of typing, your
productivity and ultimately your long term
health.
Typing Techniques
www.mrblanco.page4.me 29
 Movement vs. Stability
 Movement
 should occur primarily at the finger joints, with some
forward and backward movement of the hands to reach
for keys.
 Stability
 your whole body should be seated and supported in the
most stable position possible, with your feet rested
securely on the floor, forearms supported on the desk (or
preferably keyboard wrist support), hands held over base
of keyboard with wrists in neutral position and fingers
flexed over keys.
Typing Techniques
www.mrblanco.page4.me 30
 Touch Typing
 Typing on a keyboard with no need for looking at
fingers or keys and a trained 'finger-position' sense
for the physical location of keys, is the basis for
development of fast and accurate typing.
Typing Techniques
www.mrblanco.page4.me 31
 Getting Started
www.mrblanco.page4.me 32
 Some important rules to follow:
 Don't look at the keyboard as you type.
 When using the "shift" key to type a capital
letter or punctuation symbol, always use the
shift key on the opposite side of the
keyboard.
 Don't move your hand and other fingers any
more than necessary to reach each key.
 Be patient and practice often.
www.mrblanco.page4.me 33
 Types of Keyboard
 Wireless Keyboards
 The wireless keyboards use three basic types of
connections, viz.
 Bluetooth Keyboards
 Infrared (IR) Keyboards
 Radio Frequency Keyboards
 Wired Keyboards
 The PS/2 and USB are the two wired connections
that connect the keyboards to your desktop
computers.
 Ergonomic Keyboards
 Specially designed as per the comfort of the hands
and wrist of the keyboard user.
www.mrblanco.page4.me 34
 Types of Keyboard (cont.)
 Compact Keyboard
 Slim and usually do not have the numeric keypad
that is present on the right side of the other
keyboards.
 Internet Keyboards
 The internet keyboards have hot-keys for the home
page of the web browser, inbox and the favorites
menu on your computer
 Multimedia and Gaming Keyboards
 Designed for the convenience of the gamers and
these types of keyboards provide the required
controls on the keyboards like backlighting.
www.mrblanco.page4.me 35
 Types of Keyboard (cont.)
Virtual Keyboards
 The virtual keyboards are not actually
physical keyboards, but they are simulated
using software.
QWERTY keyboards
 The most used modern-day keyboard
layout on English-language computer and
typewriter keyboards. It takes its name
from the first six characters seen in the far
left of the keyboard's top row of letters.
www.mrblanco.page4.me 36
 Decimal
 The base-10 notational system for representing real numbers. The
expression of a number using the decimal system is called its
decimal expansion, examples of which include 1, 13, 2028, 12.1,
and 3.14159.
 Binary
 The system of representing text or computer processor
instructions by the use of the binary number system's two-binary
digits "0" and "1".
 Octal
 The base-8 number system, and uses the digits 0 to 7. Numerals
can be made from binary numerals by grouping consecutive
binary digits into groups of three (starting from the right).
 Hexadecimal
 A positional numeral system with a radix or base of 16.
www.mrblanco.page4.me 37
 Decimal To Binary Conversion
 Step 1—Divide the base 10 number by the radix (2) of the
binary system and extract the remainder (this becomes
the binary number's LSD).
 Step 2—continue the division by dividing the quotient of
step 1 by the radix (2
 Step 3—Continue dividing quotients by the radix until
the quotient becomes smaller that the divisor; then do one
more division. The remainder is our MSD.
 The remainder in step 1 is our LSD. Now rewrite the
solution, and you will see that 510 equal 1012. Now follow
the conversion of 2310 to binary:
 Step 1—Set up the problem for division.
 Step 2—Divide the number and extract the remainder.www.mrblanco.page4.me 38
 Decimal to Octal Conversion
 The conversion of a decimal number to its base 8
equivalent is done by the repeated division
method. You simply divide the base 10 number by
8 and extract the remainders. The first remainder
will be the LSD, and the last remainder will be the
MSD.
 Look at the following example. To convert 1510 to octal, set
up the problem for division.
 Since 8 goes into 15 one time with a 7 remainder, 7 then is
the LSD. Next divide 8 into the quotient (1). The result is
a 0 quotient with a 1 remainder. The 1 is the MSD.
 Now write out the number from MSD to LSD.www.mrblanco.page4.me 39
 Decimal to Hex conversion
 To convert a decimal number to base 16,
follow the repeated division procedures you
used to convert to binary and octal, only
divide by 16.
 You have to remember that the remainder
is in base 10 and must be converted to hex
if it exceeds 9.
www.mrblanco.page4.me 40
www.mrblanco.page4.me 41
 Binary to Octal conversion (cont.)
 With the use of this principle, the conversion of a
binary number is quite simple. As an example, follow
the conversion of the binary number at the beginning
of this section.
 Write out the binary number to be converted. Starting
at the radix point and moving left, break the binary
number into groups of three as shown. This grouping
of binary numbers into groups of three is called binary-
coded octal (BCO). Add 0s to the left of any MSD that
will fill a group of three.
 Next, write down the octal equivalent of each group
www.mrblanco.page4.me 42
 Binary to Hex conversion
 Convert 1110100112 to hex.
 Add 0s to the left of the MSD of the whole
portion of the number and to the right of the
LSD of the fractional part to form a group of
four.
www.mrblanco.page4.me 43
 Binary to Decimal conversion
 To convert a base 2 numbers to base 10, you must
know the decimal equivalent of each power of 2.
 The decimal value of a power of 2 is obtained by
multiplying 2 by itself the number of times
indicated by the exponent for whole numbers; for
example, 24
= 2 ´ 2 ´ 2 ´ 2 or 1610.
 For fractional numbers, the decimal value is equal
to 1 divided by 2 multiplied by itself the number
of times indicated by the exponent.
www.mrblanco.page4.me 44
 Doubling Method
 This method does not use powers.
 Start with the left-most digit of the given binary number.
For each digit as you move to the right, double your
previous total and add the current digit.
 Note the first zero (italicized) is an initial subtotal for this
conversion process.
 Like the positional notation method, this method can be
modified to convert from any base to decimal. Doubling is
used because the given number is of base 2. If the given
number is of a different base, replace the 2 in the method
with the base of the given number. For example, if the
given number is in base 37, you would replace the *2 with
*37. The final result will always be in decimal (base 10)
www.mrblanco.page4.me 45
 Octal to Binary conversion
 For some computers to accept octal data, the
octal digits must be converted to binary. This
process is the reverse of binary to octal
conversion.
 Octal to Hex conversion
 You will probably not run into many
occasions that call for the conversion of octal
numbers to hex.
www.mrblanco.page4.me 46
 Octal to Decimal Conversion
 Conversion of octal numbers to decimal is best done by
the positional notation method. This process is the one
we used to convert binary numbers to decimal.
 First, determine the decimal equivalent for each position
by multiplying 8 by itself the number of times indicated
by the exponent. Set up a bar graph of the positions and
values.
 To convert an octal number to decimal, write out the
number to be converted placing each digit under the
proper position.
 Next, multiply the decimal equivalent by the
corresponding digit of the octal number; then, add this
column of figures for the final solution
www.mrblanco.page4.me 47
 Hex to Binary conversion
 To convert a hex number to binary, set up the number in the
block format you used in earlier conversions. Below each hex
digit, write the four-digit binary equivalent.
 Hex to Octal conversion
 Just like the conversion of octal to hex, conversion of hex to octal
is a two-step procedure. First, convert the hex number to binary;
and second, convert the binary number to octal.
 Hex to Decimal Conversion
 It is difficult to comprehend the magnitude of a base 16 number
until it is presented in base 10; for instance, E016 is equal to 22410.
You must remember that usually fewer digits are necessary to
represent a decimal value in base 16.
 When you convert from base 16 to decimal, you may use the
positional notation system for the powers of 16 (a bar graph).
You can also convert the base 16 numbers to binary and then
convert to base 10. www.mrblanco.page4.me 48
 Counting in binary is similar to counting in any
other number system. Beginning with a single
digit, counting proceeds through each symbol,
in increasing order. Decimal counting uses the
symbols 0 through 9, while binary only uses
the symbols 0 and 1.
www.mrblanco.page4.me 49
 Arithmetic in binary is much like arithmetic in
other numeral systems. Addition, subtraction,
multiplication, and division can be performed
on binary numerals.
www.mrblanco.page4.me 50
www.mrblanco.page4.me 51
1 1 1 1 Carried Digits
1 1 0 1
+ 1 0 1 1 1
----------------
1 0 0 1 0 0
www.mrblanco.page4.me 52
* * * * Borrowed
1 1 0 1 1 1 0
- 1 0 1 1 1
--------------------
1 0 1 0 1 1 1www.mrblanco.page4.me 53

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Introductiontobasiccomputerconcepts

  • 1.
  • 2.  A machine capable of following instruction to alter data in a desirable way and to perform at least some of these operations without human intervention.  A computer is a programmable machine that receives input, stores and manipulates data, and provides output in a useful format.  Computer was used as an electronic device that allows inputting data and having it stored, processed, or otherwise manipulated quickly and efficiently. www.mrblanco.page4.me 2
  • 3.  The repetitive process of computation leads to people becoming bored in computing such as navigational table, tide charts, and planetary positions for astronomical almanacs. People were doing these things everyday and this is the reason why people invented computers, that is to aid in numerous computation required everyday. www.mrblanco.page4.me 3
  • 4.  The Abacus  The first computing aid that were used to help them in their computation. www.mrblanco.page4.me 4
  • 5.  The Napier’s Bone  An abacus created by John Napier for calculation of products and quotients of numbers that was based on Arab mathematics and lattice multiplication used by Fibonacci writing in the Liber Abaci. www.mrblanco.page4.me 5
  • 6.  The Slide Rule  Used primarily for multiplication and division, and also for "scientific" functions such as roots, logarithms and trigonometry, but is not normally used for addition or subtraction. www.mrblanco.page4.me 6
  • 7.  The Calculating Clock/ Schickard Calculator  Consisted of a six-digit machine that could add or subtract.  Wilhelm Schickard developed it on 1623 in Tübingen, Württemberg www.mrblanco.page4.me 7
  • 8.  The Pascaline  The first calculator or adding machine to be produced in any quantity and actually used. It could only do addition and subtraction, with numbers being entered by manipulating its dials.  designed and built by the French mathematician- philosopher Blaise Pascal between 1642 and 1644 www.mrblanco.page4.me 8
  • 9.  The Step Reckoner  The first calculator that could perform all four arithmetic operations: addition, subtraction, multiplication and division.  invented by German mathematician and philosopher Gottfried Wilhelm Leibniz around 1672 and completed 1694 www.mrblanco.page4.me 9
  • 10.  The Difference Engine  An automatic, mechanical calculator designed to tabulate polynomial functions.  By 1822 the English mathematician Charles Babbage who is considered as Father of the Computer today was proposing a steam driven calculating machine the size of a room www.mrblanco.page4.me 10
  • 11.  The Hollerith's Tabulating Machine  the electro-mechanical tabulator.  On the tabulator's desk to the right is a press-like device which would bring an array of pins into contact with a punch card. www.mrblanco.page4.me 11
  • 12.  The Mark I  The first large-scale automatic digital computer in the USA by Howard H. Aiken, built at IBM and shipped to Harvard in February 1944. www.mrblanco.page4.me 12
  • 13.  The Apple I  An early personal computer.  They were designed and hand-built by Steve Wozniak www.mrblanco.page4.me 13
  • 14.  The PDP-12  A 12 bit machine introduced in 1969. Applications included applied psychology, chemistry, patient monitoring, and industrial testing. www.mrblanco.page4.me 14
  • 15.  The IBM Personal Computer  The original version and progenitor of the IBM PC compatible hardware platform. www.mrblanco.page4.me 15
  • 16.  The Personal Computer  any general-purpose computer whose size, capabilities, and original sales price make it useful for individuals, and which is intended to be operated directly by an end user, with no intervening computer operator. www.mrblanco.page4.me 16
  • 17.  Netbooks  A branch of subnotebooks, a rapidly evolving category of small, lightweight, and inexpensive laptop computers suited for general computing and accessing Web-based applications; they are often marketed as "companion devices", i.e., to augment a user's other computer access. www.mrblanco.page4.me 17
  • 18.  Open  A task that display a document window.  Close  In a program that can be display more than one document window, to remove a window from the display.  Copy  A simple method of reproducing text or other data from a source to a destination.  Cut  To move one file in to another path or location. www.mrblanco.page4.me 18
  • 19.  Paste  Used to join files horizontally (parallel merging) by outputting lines consisting of the sequentially corresponding lines of each file specified, separated by tabs, to the standard output.  Rename  To change the name of the file.  Delete  To remove the files from the folder or into the desktop.  Web Browser  A software application used for retrieving, presenting, and traversing information resources on the World Wide Web. www.mrblanco.page4.me 19
  • 20.  Directory  A virtual container within a digital file system, in which groups of computer files and other folders can be kept and organized.   Web Page  A document or resource of information that is suitable for the World Wide Web and can be accessed through a web browser and displayed on a computer screen.  Web Site  A collection of related web pages, images, videos or other digital assets that are addressed with a common domain name or IP address in an Internet Protocol-based network. www.mrblanco.page4.me 20
  • 21.  Computer Hardware  The physical component of computer system which can be installed an operating system and a multitude of software to perform the operator’s desired functions.  Hardware Components  Input Devices Input devices are things we use to put information INTO a computer.  Output Devices Output devices are things we use to get information OUT of a computer.www.mrblanco.page4.me 21
  • 23.  Memory  Refers to devices that are used to store data or programs on a temporary or permanent basis for use in an electronic digital computer.  Microprocessors  A microprocessor incorporates most or all of the functions of a computer's central processing unit (CPU) on a single integrated circuit (IC, or microchip). www.mrblanco.page4.me 23
  • 24.  Computer Software  The intangible part of the computer system.  Operating System Software  A master control program for a computer that manages the computer’s internal functions and provides you with a means to control the computer’s operation.  Software Applications  Computer software designed to help the user to perform a singular or multiple related specific tasks. Such programs are also called software applications, applications or apps.www.mrblanco.page4.me 24
  • 25.  Peopleware  Refer to anything that has to do with the role of people in the development or use of computer software and hardware systems, including such issues as developer productivity, teamwork, group dynamics, the psychology of programming, project management, organizational factors, human interface design, and human-machine- interaction. www.mrblanco.page4.me 25
  • 26.  Operating system designed and produced by Microsoft Corporation. Similar to other operating systems, Windows makes a computer system user-friendly by providing a graphical display and organizing information so that it can be easily accessed. www.mrblanco.page4.me 26
  • 27.  Parts of a Window: The Title Bar contains the name of the application or folder. It also contains the standard Windows 98 control buttons. Drag the title bar to move a window by holding down the left mouse button as you drag the window. Control-Menu Icon allows you to minimize, maximize, restore, or close a window. Right click on the Control button to see the drop down list. Left click on the title bar to close the drop down menu. Microsoft Windows www.mrblanco.page4.me 27
  • 28.  Parts of a Window: Menu Bar provides pull down menus to access Windows 98 commands. Icons are graphic symbols used to represent an application or folder. Control Buttons allow you to minimize, maximize, restore, or close a window. Window Border is a frame around a window that allows you to resize a window. You can drag a window's border to resize a window. Microsoft Windows www.mrblanco.page4.me 28
  • 29. Ergonomics & Positioning  The positioning of your body as well as the physical layout of the work environment and equipment will significantly impact your overall efficiency of typing, your productivity and ultimately your long term health. Typing Techniques www.mrblanco.page4.me 29
  • 30.  Movement vs. Stability  Movement  should occur primarily at the finger joints, with some forward and backward movement of the hands to reach for keys.  Stability  your whole body should be seated and supported in the most stable position possible, with your feet rested securely on the floor, forearms supported on the desk (or preferably keyboard wrist support), hands held over base of keyboard with wrists in neutral position and fingers flexed over keys. Typing Techniques www.mrblanco.page4.me 30
  • 31.  Touch Typing  Typing on a keyboard with no need for looking at fingers or keys and a trained 'finger-position' sense for the physical location of keys, is the basis for development of fast and accurate typing. Typing Techniques www.mrblanco.page4.me 31
  • 33.  Some important rules to follow:  Don't look at the keyboard as you type.  When using the "shift" key to type a capital letter or punctuation symbol, always use the shift key on the opposite side of the keyboard.  Don't move your hand and other fingers any more than necessary to reach each key.  Be patient and practice often. www.mrblanco.page4.me 33
  • 34.  Types of Keyboard  Wireless Keyboards  The wireless keyboards use three basic types of connections, viz.  Bluetooth Keyboards  Infrared (IR) Keyboards  Radio Frequency Keyboards  Wired Keyboards  The PS/2 and USB are the two wired connections that connect the keyboards to your desktop computers.  Ergonomic Keyboards  Specially designed as per the comfort of the hands and wrist of the keyboard user. www.mrblanco.page4.me 34
  • 35.  Types of Keyboard (cont.)  Compact Keyboard  Slim and usually do not have the numeric keypad that is present on the right side of the other keyboards.  Internet Keyboards  The internet keyboards have hot-keys for the home page of the web browser, inbox and the favorites menu on your computer  Multimedia and Gaming Keyboards  Designed for the convenience of the gamers and these types of keyboards provide the required controls on the keyboards like backlighting. www.mrblanco.page4.me 35
  • 36.  Types of Keyboard (cont.) Virtual Keyboards  The virtual keyboards are not actually physical keyboards, but they are simulated using software. QWERTY keyboards  The most used modern-day keyboard layout on English-language computer and typewriter keyboards. It takes its name from the first six characters seen in the far left of the keyboard's top row of letters. www.mrblanco.page4.me 36
  • 37.  Decimal  The base-10 notational system for representing real numbers. The expression of a number using the decimal system is called its decimal expansion, examples of which include 1, 13, 2028, 12.1, and 3.14159.  Binary  The system of representing text or computer processor instructions by the use of the binary number system's two-binary digits "0" and "1".  Octal  The base-8 number system, and uses the digits 0 to 7. Numerals can be made from binary numerals by grouping consecutive binary digits into groups of three (starting from the right).  Hexadecimal  A positional numeral system with a radix or base of 16. www.mrblanco.page4.me 37
  • 38.  Decimal To Binary Conversion  Step 1—Divide the base 10 number by the radix (2) of the binary system and extract the remainder (this becomes the binary number's LSD).  Step 2—continue the division by dividing the quotient of step 1 by the radix (2  Step 3—Continue dividing quotients by the radix until the quotient becomes smaller that the divisor; then do one more division. The remainder is our MSD.  The remainder in step 1 is our LSD. Now rewrite the solution, and you will see that 510 equal 1012. Now follow the conversion of 2310 to binary:  Step 1—Set up the problem for division.  Step 2—Divide the number and extract the remainder.www.mrblanco.page4.me 38
  • 39.  Decimal to Octal Conversion  The conversion of a decimal number to its base 8 equivalent is done by the repeated division method. You simply divide the base 10 number by 8 and extract the remainders. The first remainder will be the LSD, and the last remainder will be the MSD.  Look at the following example. To convert 1510 to octal, set up the problem for division.  Since 8 goes into 15 one time with a 7 remainder, 7 then is the LSD. Next divide 8 into the quotient (1). The result is a 0 quotient with a 1 remainder. The 1 is the MSD.  Now write out the number from MSD to LSD.www.mrblanco.page4.me 39
  • 40.  Decimal to Hex conversion  To convert a decimal number to base 16, follow the repeated division procedures you used to convert to binary and octal, only divide by 16.  You have to remember that the remainder is in base 10 and must be converted to hex if it exceeds 9. www.mrblanco.page4.me 40
  • 42.  Binary to Octal conversion (cont.)  With the use of this principle, the conversion of a binary number is quite simple. As an example, follow the conversion of the binary number at the beginning of this section.  Write out the binary number to be converted. Starting at the radix point and moving left, break the binary number into groups of three as shown. This grouping of binary numbers into groups of three is called binary- coded octal (BCO). Add 0s to the left of any MSD that will fill a group of three.  Next, write down the octal equivalent of each group www.mrblanco.page4.me 42
  • 43.  Binary to Hex conversion  Convert 1110100112 to hex.  Add 0s to the left of the MSD of the whole portion of the number and to the right of the LSD of the fractional part to form a group of four. www.mrblanco.page4.me 43
  • 44.  Binary to Decimal conversion  To convert a base 2 numbers to base 10, you must know the decimal equivalent of each power of 2.  The decimal value of a power of 2 is obtained by multiplying 2 by itself the number of times indicated by the exponent for whole numbers; for example, 24 = 2 ´ 2 ´ 2 ´ 2 or 1610.  For fractional numbers, the decimal value is equal to 1 divided by 2 multiplied by itself the number of times indicated by the exponent. www.mrblanco.page4.me 44
  • 45.  Doubling Method  This method does not use powers.  Start with the left-most digit of the given binary number. For each digit as you move to the right, double your previous total and add the current digit.  Note the first zero (italicized) is an initial subtotal for this conversion process.  Like the positional notation method, this method can be modified to convert from any base to decimal. Doubling is used because the given number is of base 2. If the given number is of a different base, replace the 2 in the method with the base of the given number. For example, if the given number is in base 37, you would replace the *2 with *37. The final result will always be in decimal (base 10) www.mrblanco.page4.me 45
  • 46.  Octal to Binary conversion  For some computers to accept octal data, the octal digits must be converted to binary. This process is the reverse of binary to octal conversion.  Octal to Hex conversion  You will probably not run into many occasions that call for the conversion of octal numbers to hex. www.mrblanco.page4.me 46
  • 47.  Octal to Decimal Conversion  Conversion of octal numbers to decimal is best done by the positional notation method. This process is the one we used to convert binary numbers to decimal.  First, determine the decimal equivalent for each position by multiplying 8 by itself the number of times indicated by the exponent. Set up a bar graph of the positions and values.  To convert an octal number to decimal, write out the number to be converted placing each digit under the proper position.  Next, multiply the decimal equivalent by the corresponding digit of the octal number; then, add this column of figures for the final solution www.mrblanco.page4.me 47
  • 48.  Hex to Binary conversion  To convert a hex number to binary, set up the number in the block format you used in earlier conversions. Below each hex digit, write the four-digit binary equivalent.  Hex to Octal conversion  Just like the conversion of octal to hex, conversion of hex to octal is a two-step procedure. First, convert the hex number to binary; and second, convert the binary number to octal.  Hex to Decimal Conversion  It is difficult to comprehend the magnitude of a base 16 number until it is presented in base 10; for instance, E016 is equal to 22410. You must remember that usually fewer digits are necessary to represent a decimal value in base 16.  When you convert from base 16 to decimal, you may use the positional notation system for the powers of 16 (a bar graph). You can also convert the base 16 numbers to binary and then convert to base 10. www.mrblanco.page4.me 48
  • 49.  Counting in binary is similar to counting in any other number system. Beginning with a single digit, counting proceeds through each symbol, in increasing order. Decimal counting uses the symbols 0 through 9, while binary only uses the symbols 0 and 1. www.mrblanco.page4.me 49
  • 50.  Arithmetic in binary is much like arithmetic in other numeral systems. Addition, subtraction, multiplication, and division can be performed on binary numerals. www.mrblanco.page4.me 50
  • 52. 1 1 1 1 Carried Digits 1 1 0 1 + 1 0 1 1 1 ---------------- 1 0 0 1 0 0 www.mrblanco.page4.me 52
  • 53. * * * * Borrowed 1 1 0 1 1 1 0 - 1 0 1 1 1 -------------------- 1 0 1 0 1 1 1www.mrblanco.page4.me 53