Digital Electronics Unit_1.pptx

1. UNIT 1

2. What is Signal?
• A signal is an electromagnetic or electrical
current that is used for carrying data from
one system or network to another.
• In electronics and telecommunications, it
refers to any time-varying voltage that is
an electromagnetic wave which carries
information.
• There are two main types of signals:
Analog signal and Digital signal.

3. Analog and Digital Signals
• Like the data they represent, signals can be either
analog or digital.
• An analog signal has infinitely many levels of
intensity over a period of time.
• As the wave moves from value A to value B, it
passes through and includes an infinite number
of values along its path.
• A digital signal, on the other hand, can have only
a limited number of defined values.
• Although each value can be any number, it is
often as simple as 1 and O.
• The simplest way to show signals is by plotting
them on a pair of perpendicular axes.
Made By : Mr Himanshu Pabbi 3

4. • The vertical axis represents the value or
strength of a signal.
• The horizontal axis represents time. Figure 3.1
illustrates an analog signal and a digital signal.
• The curve representing the analog signal
passes through an infinite number of points.
• The vertical lines of the digital signal, however,
demonstrate the sudden jump that the signal
makes from value to value.
Made By : Mr Himanshu Pabbi 4

5. Made By : Mr Himanshu Pabbi 5
0
1
0 0 0 0

7. • Analog signal is a continuous signal in
which one time-varying quantity
represents another time-based
variable.
• These kind of signals works with
physical values and natural phenomena
such as earthquake, frequency,
volcano, speed of wind, weight,
lighting, etc.

9. • A digital signal is a signal that is used
to represent data as a sequence of
separate values at any point in time.
• It can only take on one of a fixed
number of values.
• This type of signal represents a real
number within a constant range of
values.
• Now, let’s learn some key difference
between Digital and Analog signals.

11. • A logic gate is a device that acts as a building
block for digital circuits.
• They perform basic logical functions that are
fundamental to digital circuits.
• Most electronic devices we use today will
have some form of logic gates in them

12. Logic Gates
• The seven basic logic gates includes: AND, OR,
XOR, NOT, NAND, NOR, and XNOR.
• The relationship between the input-output
binary variables for each gate can be
represented in tabular form by a truth table.
• Each gate has one or two binary input
variables designated by A and B and one
binary output variable designated by x.

13. AND GATE
• The AND gate is an electronic circuit which
gives a high output only if all its inputs are
high.
• The AND operation is represented by a dot (.)
sign.

14. OR GATE
• The OR gate is an electronic circuit which gives
a high output if one or more of its inputs are
high.
• The operation performed by an OR gate is
represented by a plus (+) sign.

16. NAND GATE
• The NOT-AND (NAND) gate which is equal to
an AND gate followed by a NOT gate.
• The NAND gate gives a high output if any of
the inputs are low.
• The NAND gate is represented by a AND gate
with a small circle on the output.
• The small circle represents inversion.

18. NOR GATE
• The NOT-OR (NOR) gate which is equal to an
OR gate followed by a NOT gate.
• The NOR gate gives a low output if any of the
inputs are high.
• The NOR gate is represented by an OR gate
with a small circle on the output.
• The small circle represents inversion.

20. Exclusive-OR/ XOR GATE
• The 'Exclusive-OR' gate is a circuit which will
give a high output if one of its inputs is high
but not both of them.
• The XOR operation is represented by an
encircled plus sign.

21. EXCLUSIVE-NOR/Equivalence GATE
• The 'Exclusive-NOR' gate is a circuit that does
the inverse operation to the XOR gate.
• It will give a low output if one of its inputs is
high but not both of them.
• The small circle represents inversion.

23. 2015
• What are universal gate? obtain EX-OR
operation with universal gates(3.5 marks)

24. Universal Logic Gates
• NAND and NOR are also known as universal
gates since they can be used to implement
any digital circuit without using any other
gate.
• This means that every gate can be created by
NAND or NOR gates only.

35. NOTE
• In nand inputs are given complement and in
nor inputs are given normal to design circuit

36. Implementation of three basic gates
using NAND and NOR gates

37. 2016
Define Boolean algebra. Give its five laws.(5
marks)

38. Boolean Algebra
• Boolean Algebra is used to analyze and
simplify the digital (logic) circuits.
• It uses only the binary numbers i.e. 0 and 1.
• It is also called as Binary Algebra or logical
Algebra.
• Boolean algebra was invented by George
Boole in 1854.

39. Rule in Boolean Algebra
• Boolean Algebra is used to analyze and
simplify the digital (logic) circuits.
• It uses only the binary numbers i.e. 0 and 1.
• It is also called as Binary Algebra or logical
Algebra.
• Boolean algebra was invented by George
Boole in 1854.

40. Rule in Boolean Algebra

41. Properties of switching algebra

44. 1.ABC(ABC+1)
ABC+1=1 using Annulment law
ABC(1)
ABC
2.A+A’+B+C
A+A’=1 using complement law
(1+B)+C
1+C using Annulment law
1

45. Reduce the following Boolean expression
(A+B+C)(A+B’+C)(A+B+C’)
Sol: A+B=X
(X+C)(A+B’+C)(X+C’)
(X+C)(X+C’)(A+B’+C)
Using distributive law we can write
(X+C.C’)(A+B’+C)
C.C’=0 so we get
(X)(A+B’+C)
Now replace X by A+B
(A+B).(A+B’+C)

46. Using distributive law
A+B.(B’+C)
A+B.B’+B.C
A+B.C

48. AB+(AC)’+AB’C (AB’C . AB=0)
AB+A’+C’+AB’C
A’+AB’C+B+C’+
A’+B’C+B+C’
A’+B+C+C’
A’+B+1 C+C’=1(USING COMPLEMENT LAW)
1

49. 2017
• State the de-morgan’s theorem and prove
them with an example(5 marks)

50. Proof of De-Morgan’s laws in boolean
algebra

55. 1. AB+CD=((AB)’.(CD)’)’
Change the
sign and
break the line

56. Change the
sign and
break the line

62. 2

63. C
Part 2

65. Drawing Logic Gates From
Boolean Expressions

66. 2019

68. Y= (A’D’CB)

69. NOR Gate

72. • Realize Y= A+BCD’ using NAND gates only

74. • Representation of Boolean expression can be
primarily done in two ways. They are as
follows:
1. Sum of Products (SOP) form
2. Product of Sums (POS) form

97. .

99. • In boolean logic

100. Product of Sums (POS)
• As the name suggests, it is formed by
multiplying(AND operation) the sum terms.
• These sum terms are also called as ‘max-
terms’.
• Max-terms are represented with ‘M’, they are
the sum (OR operation) of Boolean variables
either in normal form or complemented form.

103. • While writing POS, the following convention is
to be followed:

105. Introduction of K-Map (Karnaugh
Map)
• We can minimize Boolean expressions of 3, 4
variables very easily using K-map without
using any Boolean algebra theorems.
• K-map can take two forms Sum of Product
(SOP) and Product of Sum (POS) according to
the need of problem.
• K-map is table like representation but it gives
more information than TRUTH TABLE.
• We fill grid of K-map with 0’s and 1’s then
solve it by making groups.

106. K-Map (Karnaugh Map)
Steps to solve expression using K-map
1. Select K-map according to the number of
variables.
2. Identify minterms or maxterms as given in
problem.
3. For SOP put 1’s in blocks of K-map respective
to the minterms (0’s elsewhere).
4. For POS put 0’s in blocks of K-map respective
to the maxterms (1’s elsewhere).

107. • In K-map, the number of cells is similar to
the total number of variable input
combinations.
• For example, if the number of variables
is three, the number of cells is 23=8, and
• if the number of variables is four, the
number of cells is 24.

108. 5. Make rectangular groups containing total
terms in power of two like 2,4,8 ..(except 1) and
try to cover as many elements as you can in one
group.
6. From the groups made in step 5 find the
product terms and sum them up for SOP form.

117. 2 Variable K-map
• There is a total of 4 variables in a 2-
variable K-map.
• The following figure shows the structure of
the 2-variable K-map

119. 0

123. 3-variable K-map
• The 3-variable K-map is represented as an array
of eight cells.
• In this case, we used A, B, and C for the variable.
• We can use any letter for the names of the
variables.
• The binary values of variables A and B are along
the left side, and the values of C are across the
top.
• The value of the given cell is the binary values of A
and B at left side in the same row combined with
the value of C at the top in the same column.
• For example, the cell in the upper left corner has a
binary value of 000, and the cell in the lower right
corner has a binary value of 101.

126. SOP FORM
K-map of 3 variables
Z= ∑A,B,C(1,3,6,7)

127. • From red group we get product term—
A’C
• From green group we get product term—
AB
• Summing these product terms we get- Final
expression (A’C+AB)

129. The 4-Variable Karnaugh Map
• The 4-variable K-map is represented as an
array of 16 cells.
• Binary values of A and B are along the left
side, and the values of C and D are across
the top.
• The value of the given cell is the binary
values of A and B at left side in the same row
combined with the binary values of C and D
at the top in the same column.
• For example, the cell in the upper right corner
has a binary value of 0010, and the cell in the

132. . . .

133. K-map for 4 variables
F(P,Q,R,S)=∑(0,2,5,7,8,10,13,15)

134. • From red group we get product term—
QS
• From green group we get product term—
Q’S’
• Summing these product terms we get-
• Final expression (QS+Q’S’)

135. POS FORM
K-map of 3 variables

138. K-map of 4 variables

142. Don't Care Condition
• The "Don't care" condition says that we can use
the blank cells of a K-map to make a group of the
variables. To make a group of cells, we can use
the "don't care" cells as either 0 or 1, and if
required, we can also ignore that cell.
• We mainly use the "don't care" cell to make a
large group of cells.
• The cross(×) symbol is used to represent the
"don't care" cell in K-map. This cross symbol
represents an invalid combination. The "don't
care" in excess-3 code are 0000, 0001, 0010,
1101, 1110, and 1111 because they are invalid
combinations.
• Apart from this, the 4-bit BCD to Excess-3 code,
the "don't care" are 1010, 1011, 1100, 1101, 1110,
and 1111.

153. • We can change the standard SOP function
into a POS expression by making the
"don't care" terms the same as they are.
The missing minterms of the POS form are
written as maxterms of the POS form. In
the same way, we can change the
standard POS function into an SOP
expression by making the "don't care"
terms the same as they are. The missing
maxterms of the SOP form are written as
minterm of the SOP form

155. Number System and Base Conversions
• Electronic and Digital systems may use a
variety of different number systems, (e.g.
Decimal, Hexadecimal, Octal, Binary).
• A number N in base or radix b can be written
as:
(N)b = dn-1 dn-2 — — — — d1 d0 . d-1 d-2 — — —
— d-m
• In the above, dn-1 to d0 is integer part, then
follows a radix point, and then d-1 to d-m is
fractional part.
• dn-1 = Most significant bit (MSB)

156. • d-m = Least significant bit (LSB)

157. • An Octal Number or oct for short is the base-8
number and uses the digits 0 to 7.
• Octal numerals can be made from binary
numerals by grouping consecutive binary
digits into groups of three (starting from the
right).
• A Hexadecimal Number is a positional
numeral system with a radix, or base, of 16
and uses sixteen distinct symbols.
• It may be a combination of alphabets and
numbers.
• It uses numbers from 0 to 9 and alphabets A
to F.

158. • Decimal Number System :
If the Base value of a number system is
10. This is also known as base-10 number
system which has 10 symbols, these are:
0, 1, 2, 3, 4, 5, 6, 7, 8, 9. Position of every
digit has a weight which is a power of 10.

160. How to convert a number from one
base to another?
1. Decimal to Binary

161. • Note: Keep multiplying the fractional part
with 2 until decimal part 0.00 is obtained.
(0.25)10 = (0.01)2
• Answer: (10.25)10 = (1010.01)2

163. How to Convert from Binary to
Decimal?
• To convert a binary number to decimal we
need to perform a multiplication operation
on each digit of a binary number from right
to left with powers of 2 starting from 0 and
add each result to get the decimal number
of it.

166. 2. Binary to Decimal

167. Hexadecimal and Binary
• To convert from Hexadecimal to Binary, write
the 4-bit binary equivalent of hexadecimal.

173. • Convert the following octal numbers to
hexadecimal numbers:
137

174. • Convert the following octal numbers to
hexadecimal numbers:
1275

175. • Convert the following octal numbers to
hexadecimal numbers:
673

177. (2BD)16

179. Conversion from Binary To Hexa
Decimal number system

181. BCD or Binary Coded Decimal

184. Excess-3 Code
• In Excess-3 code, 3 is added to the individual
digit of a decimal number then these binary
equivalent are written.
• Excess-3 binary code is the only unweighted
self-complementary BCD code.
• Self-Complementary property means that the
1’s complement of an excess-3 number is the
excess-3 code of the 9’s complement of the
corresponding decimal number.

185. Converting BCD(8421) to Excess-3

186. Example
• XS-3 code for decimal number 24
• In BCD
• 2=0010
• 4=0100
Now we will add 3 to both
2+3=5 0101
4+3=7 0111
X-3 code for 24= 0101 0111

187. Self complement Excess-3 code
Complement of 0 =9
Complement of 1=8
Complement of 3=7
Complement of 4=6
Complement of 5=5
Excess-3 is only unweight code which is self
complementing code.

188. Short cut to check if code is self
complementing or not
Is 8-4-2-1 a self complementing code?
If sum is 9 it is self complementing code
8+4+2+1=15!=9 so 8-4-2-1 code is not self
complementing code.
Is 2-4-2-1 is a self complementing code?
2+4+2+1=9=9 so it is self complementing code

189. 2015
• What is gray code? Why it is important? List
features of BCD and Excess-3 codes(6 marks)

190. GRAY Code
• The gray code is a binary code.
• The binary bits are arranged in such a way
that only one binary bit changes at a time
when we make a change from any number to
the next.
• Uses of Gray codes
• Gray codes are used in Karnaugh maps.

192. Explanation of Gray Code
Starting with 0000 only 1 bit can be changed
0000 0001
Now with 0001 only 1 bit can be changed
If we change 1 than we get 0000 which is
already present so we will change 0001 to 0011
Similarly with 0011 we change one bit 0010 and
it is not present.
Similarly with other numbers.

193. Binary to Gray conversion
• The Most Significant Bit (MSB) of the gray
code is always equal to the MSB of the given
binary code.
• Other bits of the output gray code can be
obtained by XORing binary code bit at that
index and previous index.

195. Gray to binary conversion
• The Most Significant Bit (MSB) of the binary
code is always equal to the MSB of the given
gray code.
• Other bits of the output binary code can be
obtained by checking gray code bit at that
index.
• If current gray code bit is 0, then copy
previous binary code bit, else copy invert of
previous binary code bit