Digital concept
and
Number system
Chapter 1
Digital system
Digital system:
entity
can process,transfer and store any
kind of digital signals
is Composed of individual digital
logic circuits which are designed to
perform specified function
physical signal (transformation rule)
Digital signal,discrete quantities
Analog signal,continuous quantities
The difference between analog and digital lies
in the method of Encoding information
Digital logic circuit
A circuit used to process digital signal.
All function of the circuit are realized by
performing Boolean calculation or Boolean
judgment,
– It operates on numbers that represent
some real logical or arithmetic function.
Digital logic circuit
E = A+B
A4A3A2A1 B4B3B2B1
F4 F3 F2 F1
CO CI
E
BA
,0”
Digital logic circuit
The basic logic functional units that perform
primitive logic functions are called gates.
&
A
F
B
C
&
&
+
F(A,B,C)=AB+AB?C?+A?BC
Digital logic circuit
The work signal is restricted to two binary
values 0,1.
– 0 and 1 are logic value,
– They can represent the voltage level of a circuit,
1 is high level and 0 is low,
– They also can represent the two states of
transistors,conduct is defined as logic 1 and
cutoff is logic 0
Digital logic circuit
Studying the digital circuit,we are concerned with the
relationship between the input and output,the function
it provide,not the internal detail.
Digital integrated circuits,constructed from electronic
components,are designed to perform specified logic
functions.
– Simple integrated circuits contain a few logic gates is called
small-scale integration (SSI contains 0 to 9 gates)
– Medium-scale integration (MSI contains 10 to 99 gates)
– Large-scale integration (LSI contains 100 or more gates)
– Very large–scale integration (VLSI does not have a gate count
but is usually thought of as more than 1000 gates)
Digital logic circuit
Components level
First IC level (SSI)
Level four
Level three
Level five
Electronic Components,e.g,transistors,
diodes,resistors,capacitors
Function Logic Units,e.g,gates,NOT,
AND,NAND,EX-OR
Function Logic Units,e.g,adders,
counters,multiplexers
More complex Function Logic Units,e.g,
microprocessor
Complex Systems,Function Units from
levels Two through Four
Third IC level (VLSI)
Second IC level
(MSI and LSI)
Level two
Level one
Memory function
– Combinational logic circuits
– Sequential circuits
Synchronous sequential circuits
Asynchronous sequential circuits
Digital logic circuit
Some History of Digital Systems
The mathematical developments of Pascal,
Boole,DeMorgan,Babbage,and others
laid the foundations for modern digital
system.
The history of modern digital system is
also the history of computer science.
Blaise Pascal design a
mechanical adder in
1642。
Blaise Pascal (1623-1662)
The Pascaline
rear view
front view
Diagram of interior
One of the
first mechanical
computing
machines,around
1642,
In 1672,the Germany mathematician Gottfried
developed a machine to multiply and divide.
Gottfried
Wilhelm von
Leibniz
(1646-1716),
German
mathematician
and philosopher.
The Reckoner (reconstruction)
George Boole,another English
mathematician,developed a special
algebra that we now call Boolean
Algebra that has form the core of
modern logic design,
In 19th century,the Frenchman
Jacquard developed an automatic loom
for weaving cloth.
– He applied mathematical logic in the
machine design for commercial use.
Joseph Marie Jacquard?s (1752-1834) loom (织布机 )
Charles Babbage (1792-1871),
eccentric English mathematician
Charles Babbage set out
to develop an automatic
calculating machine,used
to computer value for
navigation table,that has
been recognized as the
forerunner to modern
computers.
The Difference
Engine.
The Analytical Engine.
Designed during the 1830s
– Parts remarkably similar to modern-day
computers,
– The "store"
– The "mill"
– Punch cards,
– Punch card idea picked up by Babbage from
Joseph Marie Jacquard's (1752-1834) loom,
Introduced in 1801,
Binary logic
Fixed program that would operate in real
time
Augusta Ada Byron
(1815-52).
The first programmer
In 1904,Huntington formulated a series of
mathematical statements gave Boole?s work
additional structure.
Digital system are built using electronics
that perform the functions that Boole and
Huntington formulated,
In the late 1930s,Claude Shannon
presented a paper on the use of Boolean
algebra in telephone switching,He is
considered to be the,father” of
modern digital design.
GOAL OF STUDYING
Understand the basic gate
Need not be overly concerned with the
internal electronic circuit detail
Concentrate on their use in designing higher
level function
Analyze an existing circuit to know its
function,(Give the logic statement of a
digital circuit)
Design a circuit by the statement of task to
be solved,(Give the hardware realization of
a logic problem)
and
Number system
Chapter 1
Digital system
Digital system:
entity
can process,transfer and store any
kind of digital signals
is Composed of individual digital
logic circuits which are designed to
perform specified function
physical signal (transformation rule)
Digital signal,discrete quantities
Analog signal,continuous quantities
The difference between analog and digital lies
in the method of Encoding information
Digital logic circuit
A circuit used to process digital signal.
All function of the circuit are realized by
performing Boolean calculation or Boolean
judgment,
– It operates on numbers that represent
some real logical or arithmetic function.
Digital logic circuit
E = A+B
A4A3A2A1 B4B3B2B1
F4 F3 F2 F1
CO CI
E
BA
,0”
Digital logic circuit
The basic logic functional units that perform
primitive logic functions are called gates.
&
A
F
B
C
&
&
+
F(A,B,C)=AB+AB?C?+A?BC
Digital logic circuit
The work signal is restricted to two binary
values 0,1.
– 0 and 1 are logic value,
– They can represent the voltage level of a circuit,
1 is high level and 0 is low,
– They also can represent the two states of
transistors,conduct is defined as logic 1 and
cutoff is logic 0
Digital logic circuit
Studying the digital circuit,we are concerned with the
relationship between the input and output,the function
it provide,not the internal detail.
Digital integrated circuits,constructed from electronic
components,are designed to perform specified logic
functions.
– Simple integrated circuits contain a few logic gates is called
small-scale integration (SSI contains 0 to 9 gates)
– Medium-scale integration (MSI contains 10 to 99 gates)
– Large-scale integration (LSI contains 100 or more gates)
– Very large–scale integration (VLSI does not have a gate count
but is usually thought of as more than 1000 gates)
Digital logic circuit
Components level
First IC level (SSI)
Level four
Level three
Level five
Electronic Components,e.g,transistors,
diodes,resistors,capacitors
Function Logic Units,e.g,gates,NOT,
AND,NAND,EX-OR
Function Logic Units,e.g,adders,
counters,multiplexers
More complex Function Logic Units,e.g,
microprocessor
Complex Systems,Function Units from
levels Two through Four
Third IC level (VLSI)
Second IC level
(MSI and LSI)
Level two
Level one
Memory function
– Combinational logic circuits
– Sequential circuits
Synchronous sequential circuits
Asynchronous sequential circuits
Digital logic circuit
Some History of Digital Systems
The mathematical developments of Pascal,
Boole,DeMorgan,Babbage,and others
laid the foundations for modern digital
system.
The history of modern digital system is
also the history of computer science.
Blaise Pascal design a
mechanical adder in
1642。
Blaise Pascal (1623-1662)
The Pascaline
rear view
front view
Diagram of interior
One of the
first mechanical
computing
machines,around
1642,
In 1672,the Germany mathematician Gottfried
developed a machine to multiply and divide.
Gottfried
Wilhelm von
Leibniz
(1646-1716),
German
mathematician
and philosopher.
The Reckoner (reconstruction)
George Boole,another English
mathematician,developed a special
algebra that we now call Boolean
Algebra that has form the core of
modern logic design,
In 19th century,the Frenchman
Jacquard developed an automatic loom
for weaving cloth.
– He applied mathematical logic in the
machine design for commercial use.
Joseph Marie Jacquard?s (1752-1834) loom (织布机 )
Charles Babbage (1792-1871),
eccentric English mathematician
Charles Babbage set out
to develop an automatic
calculating machine,used
to computer value for
navigation table,that has
been recognized as the
forerunner to modern
computers.
The Difference
Engine.
The Analytical Engine.
Designed during the 1830s
– Parts remarkably similar to modern-day
computers,
– The "store"
– The "mill"
– Punch cards,
– Punch card idea picked up by Babbage from
Joseph Marie Jacquard's (1752-1834) loom,
Introduced in 1801,
Binary logic
Fixed program that would operate in real
time
Augusta Ada Byron
(1815-52).
The first programmer
In 1904,Huntington formulated a series of
mathematical statements gave Boole?s work
additional structure.
Digital system are built using electronics
that perform the functions that Boole and
Huntington formulated,
In the late 1930s,Claude Shannon
presented a paper on the use of Boolean
algebra in telephone switching,He is
considered to be the,father” of
modern digital design.
GOAL OF STUDYING
Understand the basic gate
Need not be overly concerned with the
internal electronic circuit detail
Concentrate on their use in designing higher
level function
Analyze an existing circuit to know its
function,(Give the logic statement of a
digital circuit)
Design a circuit by the statement of task to
be solved,(Give the hardware realization of
a logic problem)
