BEEE - Part B - Unit 3 PPT BEEE - Part B - Unit 3 PPT.ppt

BEEE - Part B - Unit 3 PPT

1. Basic Electrical and Electronics Engineering
Part – B
Unit 3 – Digital Electronics
By
Dr.S.A.Sivakumar [Dean-Academics, ASKW]
Mr.B.Naga Rajesh(Ph.D) [AP-ECE, ASKW]

2. Overview of Number Systems
A number system is defined as a system of writing to
express numbers.
 It is the mathematical notation for representing
numbers of a given set by using digits or other symbols in a
consistent manner.

3. Types of Number Systems
The four most common number system types are:
Binary number system (Base- 2)
Decimal number system (Base- 10)
Octal number system (Base-8)
Hexadecimal number system (Base- 16)

4. Binary Number System (Base- 2)
The base 2 number system is also known as the Binary
Number System wherein, only two binary digits exist, i.e., 0
and 1.
The binary number system consists of two digits 0 and 1.
A binary digit is called a bit.
For example, 0101 is a binary number.

5. Decimal number system (Base- 10)
The decimal number system has the base (or) radix 10.
The decimal number system contain to 9 --0, 1, 2, 3, 4, 5,
6, 7, 8, 9.
Each symbol in the decimal number is called a digit. The
decimal number system is a positional weighted system;
each and every digit has a positional weight based on
position relative to the decimal point.

6. For Example,the decimal number 1457 consists of the digit 7
in the units position, 5 in the tens place, 4 in the hundreds
position, and 1 in the thousands place whose value can be
written as:
(1×10
3
) + (4×10
2
) + (5×10
1
) + (7×10
0
)
(1×1000) + (4×100) + (5×10) + (7×1)
1000 + 400 + 50 + 7
1457

7. Octal number system (Base- 8)
Its base or radix is ' 8 '.
It uses numbers from 0 to 7 to represent numbers. Octal
numbers are commonly used in computer applications.
Example: Convert 2158 into decimal.
Solution: 215
8 = 2 × 8
2
 + 1 × 8
1
 + 5 × 8
0
= 2 × 64 + 1 × 8 + 5 × 1
= 128 + 8 + 5
= 141
10

8. Hexadecimal number system (Base- 16)
The Hexadecimal number system base/radix is 16.
In the hexadecimal system, the numbers are first
represented just like in the decimal system, i.e. from 0 to 9.
Then, the numbers are represented using the alphabet
from A to F.
The below-given table shows the representation of
numbers in the hexadecimal number system.
Hexadec
imal
0 12 3 4 5 6 7 8 9 A B C D E F
Decimal0 12 3 4 5 6 7 8 9 101112131415

9. Conversion
of
Numbers

10. What we are going to explain
•Conversion between Binary & Decimal.
•Conversion between Decimal & Hexadecimal.
•Conversion between Hexadecimal & Binary.
•Conversion between Decimal & Octal.
•Conversion between Octal & Hexadecimal.
•Conversion between Binary & Octal.

11. The possibilities:
Hexadecimal
Decimal Octal
Binary
Conversion Among Bases

12. Binary to Decimal
Hexadecimal
Decimal Octal
Binary

13. •Technique
–Multiply each bit by 2
n
, where n is
the “weight” of the bit.
–The weight is the position of the
bit, starting from 0 on the right.
–Add the results.
Binary to Decimal

14. (101011)
2
=> 1 x 2
0
= 1
1 x 2
1
= 2
0 x 2
2
= 0
1 x 2
3
= 8
0 x 2
4
= 0
1 x 2
5
= 32
(43)
10
Bit “0”
EXAMPLE

15. Decimal to Binary
Hexadecimal
Decimal Octal
Binary

17. Hexadecimal
Decimal Octal
Binary
Hexadecimal to BinaryHexadecimal to Binary

18. Binary Hexadecimal
0000 0
0001 1
0010 2
0011 3
0100 4
0101 5
0110 6
0111 7
1000 8
1001 9
1010 A
1011 B
1100 C
1101 D
1110 E
1111 F

19. 
TechniqueTechnique

Convert each hexadecimal digit to a 4-bit Convert each hexadecimal digit to a 4-bit
equivalent binary representationequivalent binary representation
Hexadecimal to BinaryHexadecimal to Binary

20. Example
1 0 A F
0001 0000 1010 1111
10AF
16 = 0001000010101111
2
10AF
16
= ?
2

21. Hexadecimal
Decimal Octal
Binary
Binary to Hexadecimal

22. Binary to Hexadecimal
Technique
›Group bits in fours, starting on
right
›Convert to hexadecimal digits

23. 1010111011
2
= ?
16
10 1011 1011
2 B B

1010111011
2
= 2BB
16

24. Hexadecimal
Decimal Octal
Binary
Octal to DecimalOctal to Decimal

25. Octal to DecimalOctal to Decimal

TechniqueTechnique
•Multiply each bit by 8Multiply each bit by 8
nn
, where , where nn is the is the
“weight” of the bit.“weight” of the bit.
•The weight is the position of the bit, The weight is the position of the bit,
starting from 0 on the right.starting from 0 on the right.
•Add the resultsAdd the results

26. 724
8 =>4 x 8
0
= 4
2 x 8
1
= 16
7 x 8
2
= 448
(468)
10

27. Decimal to Octal
Hexadecimal
Decimal Octal
Binary

28. 
Technique

Divide by 8

Keep track of the remainder
Decimal to Octal

29. Example 1: Convert (127)
10
 to Octal.
Solution: 
Divide 127 by 8
127 ÷ 8= 15(Quotient) and (7)Remainder
Divide 15 by 8 again.
15 ÷ 8 = 1(Quotient) and (7) Remainder
Divide 1 by 8, we get;
1 ÷ 8 = 0(Quotient) and (1) Remainder
Since the quotient is zero now, no more division can be done. So by
taking the remainders in reverse order, we get the equivalent octal
number.
Hence, (127)
10
 = (177)
8

30. ExampleExample

31. OCTAL TO BINARY
Hexadecimal
Decimal Octal
Binary

32. Octal to Binary

33. Hexadecimal
Decimal Octal
Binary
Binary to Octal

34. Binary to Octal
•Technique
–Group bits in threes, starting on right
–Convert to octal digits

35. 1011010111
2
= ?
8
1 011 010 111
1 3 2 7

1011010111
2
= 1327
8
Example

36. Hexadecimal
Decimal Octal
Binary

37. Technique
Multiply each bit by 16
n
, where n is the
“weight” of the bit
The weight is the position of the bit, starting
from 0 on the right
Add the results
Hexadecimal to Decimal

38. Example

39. ABC
16 =>C x 16
0
= 12 x 1 = 12
B x 16
1
= 11 x 16 = 176
A x 16
2
= 10 x 256 = 2560
2748
10
ExampleExample

40. Hexadecimal
Decimal Octal
Binary
Decimal to Hexadecimal

41. Decimal to Hexadecimal
Technique
Divide by 16
Keep track of the remainder

42. Decimal to Hexadecimal

43. OCTAL TO HEXADECIMAL
Hexadecimal
Decimal Octal
Binary

44. Technique
Use binary as an intermediary

45. •.
Binary Octal
000 0
001 1
010 2
011 3
100 4
101 5
110 6
111 7

46. 1076
8
= ?
16
1 0 7 6
001 000 111 110
2 3 E
1076
8 = 23E
16
0010 0011 1110

47. Hexadecimal
Decimal Octal
Binary
HEXADECIMAL TO OCTAL

48. Technique
Use binary as an intermediary

49. Binary Hexadecimal
0000 0
0001 1
0010 2
0011 3
0100 4
0101 5
0110 6
0111 7
1000 8
1001 9
1010 A
1011 B
1100 C
1101 D
1110 E
1111 F

50. 1F0C
16 = ?
8
1 F 0 C
0001 1111 0000 1100
1 7 4 1 4
1F0C
16
= 17414
8
0 001 111 100 001 100

51. Rapid Tables
https://www.rapidtables.com/convert/number/decimal-to-hex.html?
x=15605605

52. Logic gates including Universal Gates
There are seven basic logic gates: AND, OR, XOR, NOT, NAND,
NOR and XNOR.
AND gate
The AND gate is named so because, if 0 is false and 1 is true,
the gate acts in the same way as the logical "and" operator. 
The output is "true" when both inputs are "true." Otherwise,
the output is "false." In other words, the output is 1 only when
both inputs are 1.

54. OR gate
The OR gate gets its name from behaving like the
logical inclusive "or."
The output is true if one or both of the inputs are true.
If both inputs are false, then the output is false.
In other words, for the output to be 1, at least one
input must be 1.

55. XOR gate
The XOR (exclusive-OR) gate acts in the same way as
the logical "either/or."
The output is true if either, but not both, of the inputs
are true.
The output is false if both inputs are "false" or if both
inputs are true.
Similarly, the output is 1 if the inputs are different but
0 if the inputs are the same.

57. •A NOT gate reverses the logic state. If the input
is 1, then the output is 0. If the input is 0, then
the output is 1.
NOT gate

58. NAND  gate
The NAND (Negated AND) gate operates as an AND gate
followed by a NOT gate.
 It acts in the manner of the logical operation "and"
followed by negation.
The output is false if both inputs are true.

59. NOR gate
The NOR (NOT OR) gate is a combination OR gate
followed by an inverter.
 Its output is true if both inputs are false. Otherwise,
the output is false.

60. XNOR gate
The XNOR (exclusive-NOR) gate is a combination of an
XOR gate followed by an inverter.
Its output is true if the inputs are the same and false if
the inputs are different.

61. Universal Gates

62. Boolean Algebra
•Boolean algebra is a branch of mathematics that deals
with operations on logical values with binary variables.
•Boolean variables are represented as binary numbers
to represent truths: 1 = true and 0 = false.
•Elementary algebra deals with numerical operations,
whereas Boolean algebra deals with logical operations.

63. De Morgan's Theorem 1De Morgan's Theorem 1
Theorem 1 A . B = A + BTheorem 1 A . B = A + B

64. De Morgan's Theorem 2De Morgan's Theorem 2
Theorem 2 A + B = A . BTheorem 2 A + B = A . B

65. Properties of Boolean Algebra
•T1 : Properties of 0T1 : Properties of 0
–(a) (a) 0 + A = A0 + A = A
(b) (b) 0 A = 00 A = 0
•T2 : Properties of 1T2 : Properties of 1
–(a) (a) 1 + A = 11 + A = 1
(b) (b) 1 .A = A1 .A = A

66. Properties of Boolean Algebra
•T3 : Commutative Law T3 : Commutative Law
–(a) (a) A + B = B + AA + B = B + A
(b) (b) A B = B AA B = B A
•T4 : Associate Law T4 : Associate Law
–(a) (a) (A + B) + C = A + (B + C)(A + B) + C = A + (B + C)
(b) (b) (A B) C = A (B C)(A B) C = A (B C)
•T5 : Distributive Law T5 : Distributive Law
–(a) (a) A (B + C) = A B + A CA (B + C) = A B + A C
(b) (b) A + (B C) = (A + B) (A + C)A + (B C) = (A + B) (A + C)

67. Properties of Boolean Algebra
•T6 : Identity Law T6 : Identity Law
–(a) (a) A + A = AA + A = A
(b) (b) A A = AA A = A
•T7 : Absorption Law T7 : Absorption Law
–(a) (a) A + A B = AA + A B = A
(b) (b) A (A + B) = AA (A + B) = A

68. Properties of Boolean Algebra
•T8 : Complementary LawT8 : Complementary Law
–(a) X+X’=1(a) X+X’=1
–(b) X.X’=0(b) X.X’=0
•T9 : InvolutionT9 : Involution
–(a) x’’ = x(a) x’’ = x

69. Combinational Circuits
•A combinational logic circuit is a digital circuit that
produces an output based on the current inputs,
without any internal memory or feedback. 
•The output is a function of the current inputs, and is not
dependent on the history of input signals.

70. Half Adder
A Combinational circuit that performs the
arithmetic; addition of two bits is called as half
adder.
 The output of Ex-OR gate is called Sum, while
output of AND gate is carry.
The input variables of a half-adder are called the
augends & addend bits.
The output variables are Sum & Carry.

71. Full Adder
A full-adder is a combinational circuit
that performs the addition of the three
bits is called a full-adder".
It consists of three input and two
outputs.

72. Introduction to sequential circuits
•Sequential circuits are digital circuits
that store and use previous state
information to determine their next
state.
•A combinational circuit produces an
output based on input variables only,
but a sequential circuit produces an
output based on current input and
previous output variables. 

73. Registers
•Flip flops can be used to store a single bit of binary
data (1 or 0
•N flip flops are to be connected in order to store n
bits of data.
•Shift Register is a group of flip flops used to store
multiple bits of data.
•The bits stored in such registers can be made to
move within the registers and in/out of the registers
by applying clock pulses.
  

74. An n-bit shift register can be formed by connecting n
flip-flops where each flip-flop stores a single bit of data.
The registers which will shift the bits to the left are
called “Shift left registers”.
The registers which will shift the bits to the right are
called “Shift right registers”.

75.  Shift registers are basically of following types.
Serial In Serial Out shift register
Serial In parallel Out shift register
Parallel In Serial Out shift register
Parallel In parallel Out shift register

76. Serial In Serial Out shift register
The shift register, which allows serial input (one bit after
the other through a single data line) and produces a
serial output is known as a Serial-In Serial-Out shift
register. 
The circuit consists of four D flip-flops which are
connected in a serial manner.
All these flip-flops are synchronous with each other since
the same clock signal is applied to each flip-flop. 

78. Serial In Parallel Out shift register
The shift register, which allows serial input (one bit after
the other through a single data line) and produces a
parallel output is known as the Serial-In Parallel-Out shift
register.
The output of the first flip-flop is connected to the input of
the next flip flop and so on.
All these flip-flops are synchronous with each other since
the same clock signal is applied to each flip-flop. 

80. Parallel In Serial Out shift register
The shift register, which allows parallel input (data is given
separately to each flip flop and in a simultaneous manner) and
produces a serial output is known as a Parallel-In Serial-Out shift
register.
The output of the previous flip-flop and parallel data input are
connected to the input of the MUX and the output of MUX is
connected to the next flip-flop.
All these flip-flops are synchronous with each other since the
same clock signal is applied to each flip-flop. 

82. Parallel In parallel Out shift register
The shift register, which allows parallel input (data is given separately
to each flip flop and in a simultaneous manner) and also produces a
parallel output is known as Parallel-In parallel-Out shift register.
In this type of register, there are no interconnections between the
individual flip-flops since no serial shifting of the data is required.
Data is given as input separately for each flip flop and in the same way,
output is also collected individually from each flip flop. 

84. Counters