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1. DIGITAL LOGIC
PRESENTED BY:
MAHENDRA SINGH MAHARA

2. Through This presentation, I will talked about in these topics:
Number System
Number Conversion
Analog And Digital System
Logic Gates
Boolean Algebra
K-Map

3. Number System
“The simple definition is, in digital electronics,
the number system is used for representing the
information.”

4.  Types Of Number System

5.  Types Of Number System
 There are four types of number systems exists in
digital logic:
Binary Number System
Octal Number System
Decimal Number System
Hexadecimal Number System

6. 1) Binary Number System
A binary number system is one of the four types of number
system. In computer applications, where binary numbers are
represented by only two symbols or digits, i.e. 0 (zero) and
1(one). The binary numbers here are expressed in the base-2
numeral system. For example, (101)2 is a binary number.

7. 2) octal Number System
Octal Number System has a base of eight and uses the number
from 0 to 7. The octal numbers, in the number system, are
usually represented by binary numbers when they are grouped
in pairs of three. For example, 128 is expressed as 0010102,
where 1 is equivalent to 001 and 2 is equivalent to 010.

8. 3) decimal Number System
In the decimal number system, the numbers are represented with base 10.
The way of denoting the decimal numbers with base 10 is also termed as
decimal notation. This number system is widely used in computer
applications. It is also called the base-10 number system which consists
of 10 digits, such as, 0,1,2,3,4,5,6,7,8,9. Each digit in the decimal system
has a position and every digit is ten times more significant than the
previous digit.

9. 4) hex Number System
The hexadecimal number system is a type of number system,
that has a base value equal to 16. It is also pronounced
sometimes as ‘hex’. Hexadecimal numbers are represented by
only 16 symbols. These symbols or values are 0, 1, 2, 3, 4, 5, 6,
7, 8, 9, A, B, C, D, E and F. Each digit represents a decimal
value. For example, D is equal to base-10 13.

10. Number Conversion
“As we know, the number system is a form of expressing the numbers.
In number system conversion, we will study to convert a number of
one base, to a number of another base. There are a variety of number
systems such as binary numbers, decimal numbers, hexadecimal
numbers, octal numbers, which can be exercised.”

11. NUMBER CONVERSION HELP TABLE

12.  BINARY NUMBER
CONVERSION
Binary number conversion is done to convert a number given in
the binary (base-2) number form to its equivalent value in the
others: octal, decimal and hexadecimal number form. A number
system is a format to represent numbers in a certain way. Let us
look at the conversions.

13. Binary To Octal Conversion Binary To Decimal Conversion Binary To Hexa Conversion
(101010101)2
Sol.
=(101010101)2
= (101)(010)(101)
= (525)8
(1001)10
Sol.
=(1001)10
= 1 x 2 3 + 0 x 2 2 + 0 x 2 1 + 1 x 2 0
= 8 + 0 + 0 + 1
= (9)10
(101010101)2
Sol.
= (101010101)2
= (1)(0101)(0101)
= (155)16

14.  Octal Number
Conversion
Octal number conversion is done to convert a number given in
the Octal (base-8) number form to its equivalent value in the
others: binary, decimal and hexadecimal number form. A number
system is a format to represent numbers in a certain way. Let us
look at the conversions.

15. Octal To Binary Conversion Octal To Decimal Conversion Octal To Hexa Conversion
(352.563)8
Sol.
= (352.563)8
= (011 101 010 . 101 110 011)2
= (011101010.101110011)2
(121)8
Sol.
=(121)8
=1×82+2×81+1×80
=64+16+1
=81
(56)8
Sol.
= (56)8
= (101)(110)
= (101110)2
= (10)(1110)
= (2)(14)
= (2e)16

16.  Decimal Number
Conversion
Decimal number conversion is done to convert a number given in
the decimal (base-10) number form to its equivalent value in the
others: binary, octal and hexadecimal number form. A number
system is a format to represent numbers in a certain way. Let us
look at the conversions.

17. Decimal To Binary Conversion Decimal To Octal Conversion Decimal To Hex Conversion

18. Number
Conversion
Hexadecimal number conversion is done to convert a number
given in the hexa (base-16) number form to its equivalent value
in the others: binary, octal and decimal number form. A number
system is a format to represent numbers in a certain way. Let us
look at the conversions.

19. Hexa To Binary Conversion Hexa To Octal Conversion Hexa To Decimal Conversion
(E5B)16
Sol.
= (E5B)16
= E-(14)10, 5-(5)10, B-(11)16
= (14)10 -1110
= (5)10 -0101
= (11)10 -1011
=(111001011011)2
(FF)16
Sol.
= (ff)16
= (1111)(1111)
= (11111111)2
= (11)(111)(111)
= (377)8
(ABCDEF)16
Sol.
=(ABCDEF)16
=(10x165+11x164+12x163+13x162+14x161+15x160)10
=(10485760+720896+49152+3328+224+15)10
= (11259375)10

20.  Gray Code
The gray code is the code where one bit will be differed to the
preceding number. For example, decimal numbers 13 and 14 are
represented by gray code numbers 1011 and 1001, these numbers
differ only in single position that is the second position from the
right.

21. GRAY CODE HELPER TABLE

22. Analog & Digital System

23. ANALOG SYSTEM
“An analog system is a system in which an electrical value, such
as voltage or current, represents something in the physical world.
Analog circuits use a continuous range of voltage as opposed to
discrete levels as in digital circuits.”

24. Analog Signals: Advantages and Disadvantages
 Advantages to using analog signals
• Analog signals are easier to process.
• Analog signals best suited for audio and video transmission.
• Analog signals are much higher density, and can present more refined information.
• Analog signals use less bandwidth than digital signals.
• Analog signals provide a more accurate representation of changes in physical
phenomena, such as sound, light, temperature, position, or pressure.
• Analog communication systems are less sensitive in terms of electrical tolerance.
 Disadvantages to using analog signals
• Data transmission at long distances may result in undesirable signal disturbances.
• Analog signals are prone to generation loss.
• Analog signals are subject to noise and distortion, as opposed to digital signals which
have much higher immunity.
• Analog signals are generally lower quality signals than digital signals.

25. Digital SYSTEM
“Digital systems are designed to store, process, and communicate information
in digital form. They are found in a wide range of applications, including
process control, communication systems, digital instruments, and consumer
products. The digital computer, more commonly called the computer, is an
example of a typical digital system.”

26. Digital Signals: Advantages and Disadvantages
 Advantages to using digital signals
• Digital data can be easily compressed.
• Equipment that uses digital signals is more common and fewer expensive.
• These signals turn the moving instruments free from errors.
• You can edit the sound without altering the first copy.
• Digital signals can convey information with less noise, distortion, and interference.
• Digital signals can be reproduced easily in mass quantities at comparatively low costs.
• Digital signal processing is safer because digital information are often easily encrypted and compressed.
• Digital systems are more accurate, and therefore the probability of error occurrence are often reduced by
employing error detection and correction codes.
• Digital signals can be transmitted over long distances.
 Disadvantages to using digital signals
• Sampling may cause loss of information.
• Processor speed is limited.
• Systems and processing is more complex.
• Digital systems and processing are typically more complex.

27. difference between analog and digital signals

28. Logic Gates
“A logic gate is an idealized model of computation or a physical electronic device
implementing a Boolean function, a logical operation performed on one or
more binary inputs that produces a single binary output.”

29.  Basic Gates
oNOT GATE

30.  Basic Gates
oAND GATE

31.  Basic Gates
oOR GATE

32.  Universal Gates
oNAND GATE

33.  Universal Gates
oNOR GATE

34.  Other Gates
oXOR GATE

35.  Other Gates
o XNOR GATE

36. TYPES OF GATES

37. Boolean Algebra
“Boolean algebra is a division of mathematics that deals with operations on
logical values and incorporates binary variables. Boolean algebra traces its
origins to an 1854 book by mathematician George Boole. The distinguishing
factor of Boolean algebra is that it deals only with the study of binary variables.
Most commonly Boolean variables are presented with the possible values of 1
("true") or 0 ("false"). Variables can also have more complex interpretations,
such as in set theory. Boolean algebra is also known as binary algebra.”

38. Law Of Boolean Algebra

39. Law Of Boolean Algebra

40. Truth table for minterm and maxterm

41. Standard Form in sop function

42. Standard Form in pos function

43. Karnaugh Map
“A Karnaugh map (K-map) is a pictorial method used to minimize boolean expressions
without having to use Boolean algebra theorems and equation manipulations. A K-map can be
thought of as a special version of a truth table. Using a K-map, expressions with two to four
variables are easily minimized. Expressions with five to six variables are more difficult but
achievable, and expressions with seven or more variables are extremely difficult (if not
impossible) to minimize using a K-map.”

44. Representing K-Map as this variable

45. Group-Implicant on K-Map

46. Sop sum on K-Map

47. Pos sum on K-Map

48. Thank
You