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1. Chapter 1
Introduction to Digital Systems

2. Digital computer - a digital system that performs various co
mputational tasks.
•The word “digital” implies that the information in the co
mputer is represented by variables that take a limited number
of discrete values.
•These values are processed internally by components that ca
n maintain a limited number of discrete states.
•Digital computers use the binary number system, which has t
wo digits: 0 and 1.
•A binary digit is called a bit. Information is represented in
digital computers in groups of bits.
2
1.1 Digital Computers

3. • By using various coding techniques, groups of bits can be m
ade to represent not only binary numbers but also other disc
rete symbols, such as decimal digits or letters of the alphab
et.
• A computer system is subdivided into two functional entities:
hardware and software.
3
Cont….

4. • Computer Hardware
 CPU
 Memory
• Program Memory(ROM)
• Data Memory(RAM)
 I/O Device
• Interface: 8251 SIO, 8255 PIO…..
• Input Device: Keyboard, Mouse,
Scanner
• Output Device: Printer, Plotter, Display
• Storage Device(I/O): FDD, HDD,
4
Memory
CPU
IOP
Input
Device
Output
Device
Cont….
Figure 1-1 Block Diagram of a
digital Computer

5. • Program(S/W)
 A sequence of instruction
 S/W = Program + Data
• The data that are manipulated by the
program constitute the data base
• Application S/W
 DB, word processor, Spread Sheet
• System S/W
 Consist, collection of software whose
purpose is more effective usage of
computers.
– OS, Firmware, Compiler, Device
Driver
5
Application S/W
Operating System
Computer H/W
API
ROM BIOS
Cont….

6. 6
• Computer organization
 Encompasses all physical aspects of computer systems.
E.g., control signals, memory types.
 Become familiar with how various circuits and component
s fit together to create working computer systems.
 How does a computer work?
• Computer Architecture
 Logical aspects of system implementation as seen by the p
rogrammer.
 Structure and behavior of the computer system.
 Hardware Components + ISA(Instruction set architecture)
Cont….

7. Cont….
“Hardware Components”
- CPU(Control, Data path), Memory, I/O devices
“ISA”?
- Instructions, Addressing modes, Instruction and data
formats
 How do I design a computer?
Why we study computer organization and architecture?
 Design better programs, including system software such as compil
ers, operating systems, and device drivers.
 Optimize program behavior.
 Evaluate (benchmark) computer system performance.
 Understand time, space, and price tradeoffs. 7

8. Example
•IBM(International Business Machines Corporation), SUN and I
ntel ISAs, it is possible to purchase processors which execute th
e same instructions from more than one manufacturer
•All these processors may have quite different internal organizat
ions but they all appear identical to a programmer, because their
instruction sets are the same
•Organization & Architecture enables a family of computer mod
els
 Same Architecture, but with differences in Organization
 Different price and performance characteristics.
8
Cont….

9. 9
• Computers consist of many things besides chips.
• Before a computer can do anything worthwhile, it must
also use software.
• Writing complex programs requires a “divide and
conquer” approach, where each program module solves
a smaller problem.
• Complex computer systems employ a similar technique
through a series of virtual machine layers.
1.2 The Computer Level Hierarchy

10. 10
• Each virtual machine layer is
an abstraction of the level
below it.
• The machines at each level
execute their own particular
instructions, calling upon
machines at lower levels to
perform tasks as required.
• Computer circuits
ultimately carry out the
work.
Cont….

11. 11
Level 6: The User Level
 Program execution and user interface level.
 The level with which we are most familiar.
 Run like word processors, graphics package programs or
games.
Level 5: High-Level Language Level
 The level with which we interact when we write
programs in languages such as C, Pascal, Lisp, and Java.
 Languages translated (with compiler or interpreter) to a
language the machine can understand.
Cont….

12. 12
Level 4: Assembly Language Level
 Acts upon assembly language produced from Level 5,
as well as instructions programmed directly at this
level.
Level 3: System Software Level
 Deals with operating system instructions
 Controls executing processes on the system.
 Protects system resources.
 instructions translated from assembly language to
machine language are passed through this level
unmodified.
Cont….

13. 13
Level 2: Machine Level
 Also known as the Instruction Set Architecture (ISA) Level.
 Consists of instructions that are particular to the
architecture of the machine.
 Programs written in machine language need no compilers,
interpreters, or assemblers.
Level 1: Control Level
 A control unit makes sure that instructions are decoded
and executed properly and that data is moved where and
when it should be. Control units can be microprogrammed
or hardwired.
 A microprogram is a program written in a low-level language that
is implemented by the hardware.
Cont….

14. 14
 Hardwired control units consist of hardware that directly
executes machine instructions.
 Machine instructions produced in level-2 are fed into
this microprogram, which interprets the instructions
by activating hardware suited to execute the original
instruction.
Level 0: Digital Logic Level
 This level is where we find digital circuits (the chips).
 Digital circuits consist of gates and wires.
 These components implement the mathematical logic
of all other levels.
Cont….

15. 15
• On the ENIAC, all programming was done at the digital
logic level.
• Programming the computer involved moving plugs and
wires.
• A different hardware configuration was needed to solve
every unique problem type.
Configuring the ENIAC to solve a “simple” problem r
equired many days labor by skilled technicians.
1.3 Von Neumann Model

16. 16
• Inventors of the ENIAC, John Mauchley and J.Presper
Eckert, conceived of a computer that could store
instructions in memory.
• The invention of this idea has since been ascribed to a
mathematician, John von Neumann, who was a
contemporary of Mauchley and Eckert.
• Stored-program computers have become known as
von Neumann Architecture systems.
Cont….

17. 17
• Today’s stored-program computers have the following
characteristics:
Three hardware systems:
• A central processing unit (CPU)
• A main memory system
• An I/O system
• The capacity to carry out sequential instruction
processing.
• A single data path between the CPU and main memory.
 This single path is known as the von Neumann
bottleneck.
Cont….

18. 18
• This is a general
depiction of a
von Neumann
system:
• These computers
employ a fetch-
decode-execute
cycle to run
programs as
follows . . .
Cont….

19. 19
• The control unit fetches the next instruction from
memory(RAM) using the program counter to determine
where the instruction is located.
• Control unit accesses instructions in sequence.
Cont….

20. 20
• The instruction is decoded into a language that the ALU can
understand (decoded by the control unit)
Cont….

21. 21
• Any data operands required to execute the instruction are
fetched from memory and placed into registers within the
CPU.
Cont….

22. 22
• The ALU executes the instruction and places results in
registers or memory.
• Finally instructions are stored in the main memory.
Cont….

23. 23
• Conventional stored-program computers have
undergone many incremental improvements over the
years.
• These improvements include adding specialized buses,
floating-point units, and cache memories, to name
only a few.
• But enormous improvements in computational power
require departure from the classic von Neumann
architecture.
• Adding processors is one approach.
1.4 Non-Von Neumann Model

24. 24
• In the late 1960s, high-performance computer systems
were equipped with dual processors to increase
computational throughput.
• In the 1970s supercomputer systems were introduced
with 32 processors.
• Supercomputers with 1,000 processors were built in
the 1980s.
• In 1999, IBM announced its Blue Gene system
containing over 1 million processors.
Cont….

25. 25
• Parallel processing is only one method of providing
increased computational power.
• It refers to the ability of computer system to do
multiple computational activities simultaneously with
out the need for CPU to manage and direct flow of
data and instruction
• More radical systems have reinvented the
fundamental concepts of computation.
• These advanced systems include genetic computers,
quantum computers, and dataflow systems.
• Data can be fetched at the same time.
Cont….

26. • The manipulation of binary information is done by logic
circuit called “gate”.
• Gates are blocks of hardware that produce signals of
binary 1 or 0 when input logic requirements are satisfied.
26
1.5 Logic Gates and Boolean Algebra

27. 27
Cont….

28. • In the latter part of the nineteenth century, George Boole in
censed philosophers and mathematicians alike when he sugg
ested that logical thought could be represented through math
ematical equations.
– How challenge anyone suggest that human thought could
be encapsulated and manipulated like an algebraic form
ula?
• Computers, as we know them today, are implementations of
Boole’s Laws of Thought.
28
Cont….

29. • Boolean Algebra
 is an algebra for the manipulation of objects
that can take only two values.
 Deals with binary variable(A, B, x, y: T/F
or 1/0) + logic operation(AND, OR,
NOT…)
• Boolean Function: described by an algebr
aic expression consisting of binary variables, t
he constants 0 and 1, and the logic operation sy
mbols +, . , ’
 F(x, y, z) = x + y’z
• The relationship between a function and its
binary variables can be represented in a truth
table.
29
Cont….
x y z F
0 0 0 0
0 0 1 1
0 1 0 0
0 1 1 0
1 0 0 1
1 0 1 1
1 1 0 1
1 1 1 1
2n Combination
Variable n = 3

30. • To represent a function in a truth table we need a list of the
2n combinations of n binary variables.
• A Boolean function can be transformed from an algebraic e
xpression into a logic diagram composed of AND, OR, an
d inverter gates.
30
Cont….

31. • Purpose of Boolean Algebra
 To facilitate the analysis and design of digital circuit.
Convenient Tools
 Truth table : relationship between binary variables
 Logic diagram : input-output relationship
 Find simpler circuits for the same function
• Digital computers contain circuits that implement Boolean
functions.
• The simpler that we can make a Boolean function, the smal
ler the circuit that will result.
 Simpler circuits are cheaper to build, consume less pow
er, and run faster than complex circuits.
31
Cont….

32. • With this in mind, we always want to reduce our Boolean function
s to their simplest form.
• There are a number of Boolean identities that help us to do this.
32
Cont….
Table: Basic Identities of Boolean Algebra

33. 33
• We can use Boolean identities to simplify the function:
Examples:
Cont….

34.  F= AB’ + C’D + AB’ + C’D
= x + x (let x= AB’ + C’D)
= x
= AB’ + C’D
 F= ABC + ABC’ + A’C
= AB(C + C’) + A’C
= AB + A’C
34
Cont….
Figure : Two logic diagrams for the same Boolean function.

35. Boolean functions can also be expressed in standardized or ca
nonical form.
•There are two canonical forms for Boolean expressions:
sum-of-products and product-of-sums.
Recall the Boolean product is the AND operation a
nd the Boolean sum is the OR operation.
•In the sum-of-products form, ANDed variables are ORe
d together.
For example:
•In the product-of-sums form, ORed variables are ANDe
d together:
For example: 35
Cont….

36. • It is easy to convert a function to
sum-of-products form using its tr
uth table.
• We are interested in the values of
the variables that make the functi
on true (=1).
• Using the truth table, we list the v
alues of the variables that result i
n a true function value.
• In each product term, you must th
en complement any variables that
are 0 for that row.
• Each group of variables is then O
Red together.
36
Cont….

37. • The sum-of-products for our function is:
37
We note that this function is not
in simplest terms. Our aim is onl
y to rewrite our function in cano
nical sum-of-products form.
Cont….

38. DeMorgan’s law – it provides an easy way of finding the com
plement of a Boolean function.
Recall DeMorgan’s law:
•Replace each variable by its complement and change all AN
Ds to ORs and all ORs to ANDs.
•Thus, we find the complement of:
38
Cont….

39. Map Simplification
•Karnaugh Map(K-map)-is map method for simplifying
Boolean expressions.(graphical representation)
•is a matrix consisting of rows and columns that represent the
output values of a Boolean function.
•The output values placed in each cell are derived from the mi
nterms of a Boolean function.
•A minterm is a product term that contains all of the function’
s variables exactly once, either complemented or not complem
ented.
39
Cont….

40. • For example, the minterms for a function having the inputs x
and y are:
• Consider the Boolean function,
• Its minterms are:
40
Cont….

41. • Similarly, a function having three inputs, has the minterms
that are shown in this diagram.
41
Cont….

42. • A K-map has a cell for each minte
rm.
• This means that it has a cell for eac
h line for the truth table of a functi
on.
• The truth table for the function F(x,
y) = xy is shown at the right along
with its corresponding K-map.
42
Cont….

43. • As another example, we give the tr
uth table and K-map for the functi
on, F(x,y) = x + y at the right.
• This function is equivalent to OR
of all of the minterms that have a v
alue of 1. Thus:
43
Cont….

44. • We reduce our complicated expression to its simplest term
s by finding adjacent 1s in the Kmap that can be collected i
nto groups that are powers of two.
• In our example, we have two such groups.
 Can you find them?
• The best way of selecting two groups of 1s from our simpl
e Kmap is shown below.
• We see that both groups are powers
of two and that the groups overlap.
44
Cont….

45. The rules of Kmap simplification are:
• Groupings can contain only 1s; no 0s.
• Groups can be formed only in the same row or in the sa
me column (diagonal groups are not allowed).
• The number of 1s in a group must be a power of 2 even
if it contains a single 1.
• The groups must be made as large as possible.
• Groups can overlap and wrap around the sides of the K
map.
45
Cont….

46. • A Kmap for three variables is constructed as shown in the
diagram below.
• We have placed each minterm in the cell that will hold its
value.
Notice that the values for the yz combination at the top of th
e matrix form a pattern that is not a normal binary sequen
ce. (The input values for the Kmap must be ordered so tha
t each minterm differs in only one variable from each neig
hbor)
46
Cont….

47. • Thus, the first row of the Kmap contains all minterms wher
e x has a value of zero.
• The first column contains all minterms where y and z both
have a value of zero.
47
Cont….

48. • Consider the function:
• Its Kmap is given below.
 What is the largest group of 1s that is a power of 2?
48
Cont….

49. • This grouping tells us that changes in the variables x and y
have no influence upon the value of the function: They are
irrelevant.
• This means that the function,
reduces to F(x) = z.
49
Cont….

50. • Now for a more complicated Kmap. Consider the function
:
• Its Kmap is shown below. There are (only) two groupings
of 1s.
 Can you find them?
50
Cont….

51. • In this Kmap, we see an example of a group that wraps arou
nd the sides of a Kmap.
• This group tells us that the values of x and y are not relevan
t to the term of the function that is encompassed by the grou
p.
What does this tell us about this term of the function?
51
What about the
green group in t
he top row?
Cont….

52. 52
Recall that we had si
x minterms in our o
riginal function!
Cont….

53. • Our model can be extended to accommodate the 16 minter
ms that are produced by a four-input function.
• This is the format for a 16-minterm Kmap.
53
Cont….

54. • We have populated the Kmap shown below with the nonze
ro minterms from the function:
 Can you identify (only) three groups in this Kmap?
54
Recall that gr
oups can overl
ap.
Cont….

55. • Our three groups consist of:
 A purple group entirely within the Kmap at the right
.
 A pink group that wraps the top and bottom.
 A green group that spans the corners.
• Thus we have three terms in our final function:
55
Cont….

56. Integrated Circuits
• is a small silicon semiconductor crystal called a chip , cont
aining the electronic components for the digital gates.
•The various gates are interconnected inside the chip to form
the required circuit.
•IC’s are the tiny electronics circuit used to perform the sever
al operations like Amplifier, timer, counter, oscillator, microc
ontroller or a computer memory.
56
1.6. Common digital components

57. • As the technology of ICs has improved, the number of g
ates that can be put in a single chip has increased consid
erably.
• The differentiation between those chips that have a few
internal gates and those having hundreds or thousands
of gates is made by a customary reference to a package a
s being either a small, medium, or large-scale integration
device.
 SSI(Small Scale Integration Device)-contain several indep
endent gates in a single package. The inputs and outputs o
f the gates are connected directly to the pins in the packa
ge. The number of gates is usually less than 10 and is li
mited by the number of pins available in the .
57
Cont….

58.  MSI(Medium-scale integration)- have a complexity of appro
ximately 10 to 200 gates in a single package. They usually
perform specific elementary digital functions such as deco
ders, adders, and registers.
 LSI (Large-scale integration) - contain between 200 and a f
ew thousand gates in a single package. They include digita
l systems, such as processors, memory chips, and progra
mmable modules.
 VLSI(Very Large Scale Integration)- contain thousands of
gates within a single package. Examples are large mem
ory arrays and complex microcomputer chips.
58
Cont….

59. Registers
•is a group of flip-flops with each flip-flop capable of storin
g one bit of information.
•They can be implemented using D flip-flops.
•One D flip-flop is equivalent to a 1-bit register, so a collectio
n of D flip-flops is necessary to store multi-bit values.
 A 32-bit register requires 32 D flip-flops.
These collections of flip-flops must be clocked to work in un
ison. At each pulse of the clock, input enters the register and c
annot be changed (and thus is stored) until the clock pulses ag
ain.
59
Cont….

60. Binary Counter
•It goes through a predetermined sequence of states as the cloc
k pulses.(follows the binary number sequence )
•Counters are found in almost all equipment containing digi
tal logic.
•They are used for counting the number of occurrences of an
event and are useful for generating timing signals to control t
he sequence of operations in digital computers.
60
Cont….

61. Memory Units
• is a collection of storage cells together with associated circ
uits needed to transfer information in and out of storage.
•It stores binary information in groups of bits called words.
•A memory word is a group of l's and 0's and may repres
ent a number, an instruction code, one or more alphanu
meric characters, or any other binary-coded information.
61
Cont….

62. • A connected arrangement of logic gates with a set of
inputs and outputs.
• It produces a specified output at the instant when input val
ues are applied.
i0 f0
i1 f1
in fm
62
1.7. Combinational Circuits
Combinational
Circuits
(Logic Gates)
...
...

63. Half-Adder
The most basic digital arithmetic circuit is the addition of tw
o binary digits.
 A combinational circuit that performs the arithmetic additio
n of two bits is called a half-adder.
63
Design Example

64. Full Adder
 We can change our half adder into to a full adder by includin
g gates for processing the carry bit.
 Full adder is a combinational circuits that forms the
arithmetic sum of three input bit(Carry considered).
64
Cont….

65. Decoder
a combinational circuit that converts binary information fr
om the n coded inputs to a maximum of 2n unique outputs
.
Decoders have a wide variety of applications in digital system
s such as data demultiplexing, digital display, digital to analog
converting, memory addressing.
65
This is a block
diagram for a
decoder.
Cont….

66. • This is what a 2-to-4 decoder looks like on the inside.
66
If x = 0 and y = 1,
which output line
is enabled?
Cont….

67. Multiplexer(data selector)
It selects a single output from several inputs.
The particular input chosen for output
is determined by the value of the
multiplexer’s control lines.
The term multiplex means “many into one.
67
Cont….

68. 68
1.8. Sequential Circuits
Combinational
Circuit
Flip-Flops
Input
Output
Clock
• A sequential circuit is an interconnection of F/F and Gate
Sequential circuits are broadly classified into two main categories,
known as synchronous or clocked and asynchronous or unclock
ed sequential circuits, depending on the timing of their signals.
 synchronous sequential circuit
Is a sequential circuit whose behavior can be defined from the knowledge o
f its signal at discrete instants of time.
Combinational Circuit = Gate
Sequential Circuit = Gate + F/F

69. In these systems, the memory elements are affected only at di
screte instants of time.
•The synchronization is achieved by a timing device known a
s a system clock.
•State changes are controlled by clocks.
 A “clock” is a special circuit that sends electrical pulses
through a circuit.
•Clocks produce electrical waveforms such as the one shown
below
69
Cont….

70.  Asynchronous sequential circuit
• Is a sequential in which they become active the moment
any input value changes. (The output will be affected w
henever the input changes)
• There is no need to wait for a clock pulse.
• Asynchronous circuits are faster than synchronous seque
ntial circuits. However, in an asynchronous circuit, even
ts are allowed to occur without any synchronization. An
d in such a case, the system becomes unstable.
• Since the designs of asynchronous circuits are more tedi
ous and difficult, their uses are rather limited.
70
Cont….

71. • In clocked sequential circuits, the transition from present
state to next state is activated by the presence of a cloc
k signal.
• Circuits can change state on the rising edge, falling edge, or
when the clock pulse reaches its highest voltage.
• Circuits that change state on the rising edge, or falling edge
of the clock pulse are called edge-triggered.
• Level-triggered circuits change state when the clock voltage
reaches its highest or lowest level. 71
Cont….

72. • To retain their state values, sequential circuits rely on feed
back.
• Feedback in digital circuits occurs when an output is loope
d back to the input.
• A simple example of this concept is shown below.
– If Q is 0 it will always be 0, if it is 1, it will always be1.
Why?
72
Cont….

73. Flip-Flop
 The storage elements employed in clocked sequential
circuit which are capable of storing binary information.
 It can have only two states, either the 1 state or the 0 stat
e.
 The state of Q is called the state of the flip-flop, wherea
s the state of Q' is called the complementary state of the
flip-flop.
73
Cont….

74.  The two outputs are complementary to each other. If Q is
1 i.e., Set, then Q' is 0; i.e., Reset, then Q' is 1. That mean
s Q and Q' cannot be at the same state simultaneously. If it
happens by any chance, it violates the definition of a flip-fl
op and hence is called an undefined condition.
The most common types of flip-flops are presented belo
w.
SR Flip-Flop
74
Cont….

75. • The behavior of an SR flip-flop is described by a characteri
stic table.
• Q(t) means the value of the output at time t. Q(t+1) is the
value of Q after the next clock pulse.
• We can describe any flip-flop by using a characteristic tab
le, which indicates what the next state should be based on t
he inputs and the current state
75
Cont….

76. • The SR flip-flop actually h
as three inputs: S, R, and it
s current output, Q.
• Thus, we can construct a tr
uth table for this circuit, as
shown at the right.
• Notice the two undefined
values. When both S and
R are 1, the SR flip-flop is
unstable.
76
The SR flip-flop should not be pulsed when
S = R = 1 since it produces an indeterminate next state .
Cont….

77. JK Flip-Flop
•The SR flip-flop can be modified to provide a stable state when b
oth inputs are 1.
This modified flip-flop is called a JK flip-flop, shown at the right.(“JK
” is in honor of Jack Kilby)
Fig: Modified SR flip-flop
•The characteristic table indicates that
the flip-flop is stable for all inputs. 77
Cont….

78. D Flip-Flop
•the output of the flip-flop r
emains the same during subs
equent clock pulses.
•The output changes only w
hen the value of D changes.
• The D flip-flop is the fund
amental circuit of comput
er memory.
 D flip-flops are usually
illustrated using the bl
ock diagram shown bel
ow.
78
Cont….