Digital Logic Presentation || Mahendra Mahara

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The simple definition is, in digital
electronics, the number system is used for
representing the information.
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• Types Of Number System

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• Types Of Number System

• There are four types of number systems exists in
  digital logic

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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.
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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.
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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.
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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.
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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.
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• 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.
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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
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• 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.
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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 182281180 64161 81 (56)8 Sol. (56)8 (101)(110) (101110)2 (10)(1110) (2)(14) (2e)16
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• 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.
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Decimal To Binary Conversion Decimal To Octal Conversion Decimal To Hex Conversion

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• Hexadecimal 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.
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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 (10x16511x16412x16313x16214x16115x160)10 (1048576072089649152332822415)10 (11259375)10
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• 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.
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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.
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• 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.

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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.
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• 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.

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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.
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• Basic Gates

• NOT GATE

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• Basic Gates

• AND GATE

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• Basic Gates

• OR GATE

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• Universal Gates

• NAND GATE

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• Universal Gates

• NOR GATE

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• Other Gates

• XOR GATE

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• Other Gates

• XNOR GATE

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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.
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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.
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Thank You