The document discusses the different number systems used in computers. It introduces the four main types of number systems: binary, decimal, octal, and hexadecimal. It explains that computers understand numbers in the form of binary digits. The other number systems are introduced to make working with binary numbers easier for humans. The hexadecimal system in particular is used as a shorthand because each hexadecimal digit can represent a group of 4 binary digits. Understanding number systems is important for understanding how computers work with numeric data and instructions.

1. NUMBER SYSTEM
TYPES OF COMPUTER NUMBER SYSTEM
Mark P. Villaplaza
BSME-2B

2. INTRODUCTION
Computers understand machine language only. Every
instruction given to the computer gets converted into machine
language. This language comprises of numbers. To understand
it, one has needed to have a better understanding of the number
system. The number system is a way to represent or express
numbers. You have heard of various types of number systems
such as the whole numbers and the real numbers. But in the
context of computers, we define other types of number systems.
In this lesson, we are going to discuss the 4 types of computer
number systems and their comparison through a conversion
table.
2
NUMBER SYSTEM
TYPES OF COMPUTER NUMBER SYSTEM

3. Hello!
I am Mark P. Villaplaza
BSME-2B
I am here because I love to give presentations.
You can find me at:
markovillaplaza279@gmail.com
3

4. LEARNING OBJECTIVES:
At the end of this lesson, you will be able to:
✓ Identify different computer number system and their comparison
✓ Define base, weight, radix point, and binary point
✓ Identify the two states of a digital circuit in binary numbers
✓ Understand why the hexadecimal number system is used in the
computer world
4

5. PRE-TEST
ACTIVITIES
ABSTRACTION
APPLICATION
REFLECTION/LEARNING INSIGHTS
Let’s do it!

6. PRE-TEST
ACTIVITIES
ABSTRACTION
APPLICATION
REFLECTION/LEARNING INSIGHTS
Let’s do it!

7. PRE-TEST
7
Let us have a

8. 1. The hexadecimal digits are 1 to 0 and A to _ .
a. Z
8
PRE-TEST
b. J c. G d. F

9. 1. The hexadecimal digits are 1 to 0 and A to _ .
a. Z
9
PRE-TEST
b. J c. G d. F

10. 2. How many bytes are there in 1011 1001 0110
1110 numbers?
a. 16
10
b. 2 c. 4 d. 8
PRE-TEST

11. 2. How many bytes are there in 1011 1001 0110
1110 numbers?
a. 16
11
b. 2 c. 4 d. 8
PRE-TEST

12. 3. 26 is equivalent to _ in decimal numbers.
a. 64
12
b. 3 c. 12 d. 8
PRE-TEST

13. 3. 26 is equivalent to _ in decimal numbers.
a. 64
13
b. 3 c. 12 d. 8
PRE-TEST

14. 4. Decimal number 8 is 1000 in binary numbers
and in octal numbers.
a. 8
14
b. 7 c. 1 d. 10
PRE-TEST

15. 4. Decimal number 8 is 1000 in binary numbers
and in octal numbers.
a. 8
15
b. 7 c. 1 d. 10
PRE-TEST

16. PRE-TEST
16
Let us have a

17. PRE-TEST
ACTIVITIES
ABSTRACTION
APPLICATION
REFLECTION/LEARNING INSIGHTS
Let’s do it!

18. Correct!
18
NEXT No.2
PRE-TEST

19. 2. How many bytes are there in 1011 1001 0110
1110 numbers?
a. 16
19
b. 2 c. 4 d. 8
PRE-TEST

20. 2. How many bytes are there in 1011 1001 0110
1110 numbers?
a. 16
20
b. 2 c. 4 d. 8
PRE-TEST

21. Correct!
21
NEXT No.3
PRE-TEST

22. 3. 26 is equivalent to _ in decimal numbers.
a. 64
22
b. 3 c. 12 d. 8
PRE-TEST

23. 3. 26 is equivalent to _ in decimal numbers.
a. 64
23
b. 3 c. 12 d. 8
PRE-TEST

24. Correct!
24
NEXT No. 4
PRE-TEST

25. 4. Decimal number 8 is 1000 in binary numbers
and in octal numbers.
a. 8
25
b. 7 c. 1 d. 10
PRE-TEST

26. 4. Decimal number 8 is 1000 in binary numbers
and in octal numbers.
a. 8
26
b. 7 c. 1 d. 10
PRE-TEST

27. Correct!
27
HOME
How many correct answer you have got?
PRE-TEST

28. PRE-TEST
ACTIVITIES
ABSTRACTION
APPLICATION
REFLECTION/LEARNING INSIGHTS
Let’s do it!

29. Do It ONE MORE TIME!
29
BACK
PRE-TEST

30. 1. The hexadecimal digits are 1 to 0 and A to _ .
a. Z
30
PRE-TEST
b. J c. G d. F

31. 1. The hexadecimal digits are 1 to 0 and A to _ .
a. Z
31
PRE-TEST
b. J c. G d. F

32. Do It ONE MORE TIME!
32
BACK
PRE-TEST

33. 2. How many bytes are there in 1011 1001 0110
1110 numbers?
a. 16
33
b. 2 c. 4 d. 8
PRE-TEST

34. 2. How many bytes are there in 1011 1001 0110
1110 numbers?
a. 16
34
b. 2 c. 4 d. 8
PRE-TEST

35. Do It ONE MORE TIME!
35
BACK
PRE-TEST

36. 3. 26 is equivalent to _ in decimal numbers.
a. 64
36
b. 3 c. 12 d. 8
PRE-TEST

37. 3. 26 is equivalent to _ in decimal numbers.
a. 64
37
b. 3 c. 12 d. 8
PRE-TEST

38. Do It ONE MORE TIME!
38
BACK
PRE-TEST

39. 4. Decimal number 8 is 1000 in binary numbers
and in octal numbers.
a. 8
39
b. 7 c. 1 d. 10
PRE-TEST

40. 4. Decimal number 8 is 1000 in binary numbers
and in octal numbers.
a. 8
40
b. 7 c. 1 d. 10
PRE-TEST

41. PRE-TEST
ACTIVITIES
ABSTRACTION
APPLICATION
REFLECTION/LEARNING INSIGHTS
Let’s do it!

42. ACTIVITIES
42
Let us have

43. FACTS
If the last digit of a binary number
is 1(one), the number is odd; if it’s
0(zero), the number is even.
43
ACTIVITIES

44. Before going further with our lesson, let’s have a quick exercise
to assess your knowledge regarding the things we are going to
discuss later.
2.1.1
In your own words, define the following terminologies:
1. Decimal
2. Binary
3. Hexadecimal
4. Octagonal
44
ACTIVITY

45. 45
Congratulations!
You have completed the first two
tasks. For you to completely
understand our lesson, you need to
analyze and reflect on your previous
activities.
2.1.1
ACTIVITY

46. 2.1.2
46
Complete each statement based on your experience.
The activities above made me remember …
It made me think and realize that…
Now, I want to learn and understand more on…
ACTIVITY

47. 47
That is great!
You may continue This Session by
clicking the Home bUttoN below..
2.1.1
ACTIVITY
HOME

48. PRE-TEST
ACTIVITIES
ABSTRACTION
APPLICATION
REFLECTION/LEARNING INSIGHTS
Let’s do it!

49. ABSTRACTION
49
Let us have aN

50. NUMBER SYSTEM
When we type some letters or words, the computer translates them in numbers
as computers can understand only numbers. A computer can understand
positional number system where there are only a few symbols called digits and
these symbols represent different values depending on the position they occupy
in the number.
50
ABSTRACTION

51. A value of each digit in a number can be determined using
1. The digit
2. The position of the digit in the number
3. The base of the number system (where base is
defined as the total number of digits available in the
number system).
51
ABSTRACTION

52. 52
As mention earlier, the technique to
represent and work with numbers is
called the number system.
ABSTRACTION

53. THE numbers
system
53
ABSTRACTION

54. 4 TYPES of number system
Hexadecimal
Number
System
Octal
Number
System
Decimal
Number
System
54
Binary
Number
System
ABSTRACTION
MORE

55. 55
Decimal
Number
System
- This is the most commonly used number system in the
world.
- It uses ten different characters to show the values of
numbers.
- The are ten different characters uses in a system that is
called the base 10 system.
- The base of a number system tells how many different
characters are used.
- The mathematical term for the base of a number system
is radix.
- The symbols used are called Arabic numerals
consisting of 10 symbols (0, 1, 2, 3, 4, 5, 6, 7, 8, 9). The
radix or the base of a decimal system is ten (10).
ABSTRACTION

56. 4 TYPES of number system
Hexadecimal
Number
System
Octal
Number
System
Decimal
Number
System
56
Binary
Number
System
ABSTRACTION
MORE

57. 57
- this system is simpler than the decimal number system
because it uses only two characters.
- The binary number system is used in digital electronics
because digital circuits have only two states (two signal
levels).
- This is ideal for computer processing because the “1” is
used to denote electrical pulse or signal and “0” is used
to denote the absence of such signal.
- The binary notations “0” and “1” are called bits, which is
an acronym for BInarydigiTs. Often when referring to
binary numbers you will hear the terms “LSB” (least
significant bit) and “MSB” (most significant bit).
Binary
Number
System
ABSTRACTION

58. 58
Binary
Number
System
- These are very much like the terms we use when speaking of
decimal numbers. In decimal numbers, we refer to the most
significant digit (MSD) and the least significant digit (LSD).
- The LSB is the bit with the least weight. The MSB is the bit with
the greatest weight. Normally, binary numbers are shown with
the MSB as the leftmost bit.
Example:
Figure 2.1.1 Parts of a Number
The radix or the base of a binary system is two (2).
ABSTRACTION

59. Some other common figures, which are used in special situations, are the following:
59
One State Opposite State
Off On
Low High
Open Closed
ABSTRACTION

60. Some other common figures, which are used in special situations, are the following:
60
ABSTRACTION

61. 4 TYPES of number system
Hexadecimal
Number
System
Octal
Number
System
Decimal
Number
System
61
Binary
Number
System
ABSTRACTION
MORE

62. Octal
Number
System
- This system is a shorthand method for
replacing groups of binary digits by a single
octal digit to reduce the number of digits
required in representing any number.
- -It has a radix or base of eight (8), consisting
of 0, 1, 2, 3, 4, 5, 6, 7.
ABSTRACTION

63. 4 TYPES of number system
Hexadecimal
Number
System
Octal
Number
System
Decimal
Number
System
63
Binary
Number
System
ABSTRACTION
MORE

64. - refers to the base 16 number system in which
16 different characters are used, consisting of
0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F.
Hexadecimal
Number
System
ABSTRACTION

65. 4 TYPES of number system
Hexadecimal
Number
System
Octal
Number
System
Decimal
Number
System
65
Binary
Number
System
ABSTRACTION
MORE

66. We know that no electronic system uses 16
different levels in the way that binary
electronics uses two different levels. This
system is not required by the machines. It
is a convenience for people. The
hexadecimal numbering system is used in
the world of computers as a shorthand
technique.
66
Why is the hexadecimal numbering system used?
ABSTRACTION

67. You can see that there is a very real problem
because of their length.
For example, many computers use an 8-bit word.
That is, when they work with a binary
number, it has 8 bits. This 8-bit number has just as
many characters as the decimal numbers from any
value from 0 to 99,999,999.
The binary number that represents a large
decimal number like 99,999,999 is very long. The
binary version of 99,999,999 is 27 bits long. Such a
long number is very difficult to read.
So, the hexadecimal numbering system is
used as a shorthand method to reduce the length of
binary numbers.
67
Stop and
think of
some of the
common
uses for
binary
numbers.
ABSTRACTION

68. 68
Sixteen, as we know, is the
fourth power of 2. That is,
16 = 24 . Each of the 16
hexadecimal characters (0
through F) can be
represented by a 4-bit
binary number, that is,
00002 to 11112. This means
that one hexadecimal
character can serve as a
shorthand notation for a 4-
bit binary number.
ABSTRACTION

69. 69
AWESOME!
You may continue This Session by
clicking the Home button below..
HOME
ABSTRACTION

70. 70
AWESOME!
You may continue This Session by
clicking the Home bUttoN below..
HOME
ABSTRACTION

71. PRE-TEST
ACTIVITIES
ABSTRACTION
APPLICATION
REFLECTION/LEARNING INSIGHTS
Let’s do it!

72. APPLICATION
72
Let us have aN

73. You can do it!
In the previous section, you just learn the four
common types of number systems, their meaning,
and importance.
To retain those learning you have acquired, you need
to make a Powerpoint Presentation (ppt) about our
lesson.
Your presentation should be creative enough for it to
be informative as well as interesting for the readers.
73
APPLICATION

74. 74
SEEMS LIKE YOU KNOW EVERYTHING about this lesson!
Keep Up the good work!
You may continue This Session by clicking the Home bottom below..
HOME
APPLICATION

75. 75
SEEMS LIKE YOU KNOW EVERYTHING about this lesson!
Keep Up the good work!
You may continue This Session by clicking the Home bottom below..
HOME
APPLICATION

76. PRE-TEST
ACTIVITIES
ABSTRACTION
APPLICATION
REFLECTION/LEARNING INSIGHTS
Let’s do it!

77. REFLECTION/
LEARNING INSIGHTS
77
Let us have your

78. Almost Done!
To assess the learning you have acquired from our lessons
and activities, write an essay answering the question below:
“Why do we need a
different number system?”
78
REFLECTION/LEARNING INSIGHTS

79. 79
You have done all of your task today!
You deserve a good TIME!
You may exit This Session by clicking the Exit button and If you wish
to go back in some part of this presentation, just click the home
button
HOME EXIT

80. 80
You have done all of your task today!
You deserve a good TIME!
You may exit This Session by clicking the Exit button and If you wish
to go back in some part of this presentation, just click the home
button
HOME EXIT

81. Thanks!
Any questions?
You can find me at:
Markovillaplaza279@gmail.com
81

82. Credits
Module of Computer Programming by Alexander Aquino
file:///Users/markovillaplaza/Desktop/ACFrOgBj3bYTyKHsb9jAUpJ4VzYUP8hNZv1GjssaZFhJy6zd31T8v
udb8a4VI8c9HvfFAMAP2XdX7nteGgHUC5fxzkHNncMzeQYeTflKirtS7cNMB0c0GVsYXEAbFPy8WxpLwb
A1QGKAZd_5zmIk.pdf
Gifs:
https://www.google.com/search?q=computer+number+system+gif&tbm=isch&ved=2ahUKEwjHz5LSyJ
buAhXyNKYKHQHqDEQQ2cCegQIABAA&oq=computer+number+system+gif&gslcp=CgNpbWcQA1DUYVi
DZmCyZ2gAcAB4AIABTIgB1AGSAQEzmAEAoAEBqgELZ3dzLXdpei1pbWfAAQE&sclient=img&ei=FK39X8
f1OPLpmAWB1LOgBA&bih=721&biw=1280#imgrc=urJ2eIW-ZKws2M
82

83. ATTRIBUTES
83

84. Presentation design
This presentations uses the following typographies and colors:
Titles: Amatic SC
Body copy: Merriweather
You can download the fonts on these pages:
https://www.fontsquirrel.com/fonts/amatic
https://www.fontsquirrel.com/fonts/merriweather
Light gray #f5f6f7
Dark gray #95a5a6
Navy #2c3e50
Salmon #f55d4b
You don’t need to keep this slide in your presentation. It’s only here to serve you as a design guide if you
need to create new slides or download the fonts to edit the presentation in PowerPoint®
84

85. SlidesCarnival icons are
editable shapes.
This means that you can:
● Resize them
without losing
quality.
● Change fill color
and opacity.
Isn’t that nice? :)
85

86. Diagrams and infographics
86

87. Now you can use any emoji as an icon!
And of course it resizes without losing quality and you can
change the color.
How? Follow Google instructions
https://twitter.com/googledocs/status/730087240156643328
✋👆👉👍👤👦👧👨👩👪💃🏃💑❤
😂😉😋😒😭👶😸🐟🍒🍔💣📌📖🔨
🎃🎈🎨🏈🏰🌏🔌🔑 and many more...
😉
87