Transcript Operating Systems

Digital Logic Circuits
(Part 1)
Computer Architecture
(Fall 2006)
Electronics for Boolean Algebra
• Interconnected set of Transistors called Circuits
– Transistors are Electronic Switches
• Turn “On” or “Off”
– Depending on input voltages
– Used to implement Boolean expressions
(A•B)+C
A
C
B
Transistor
Logic Gates
• Developing large circuits is complex
– Drawing many transistors is cumbersome
– Makes the circuit diagram unwieldy
• Hard to illustrate and comprehend
• Solution: Logic Gates
– Abstract notation for common logic circuits
• Functionally similar to set of transistors
– Simpler to develop and use
Basic Gates
• Corresponding to basic operations in Boolean
Algebra
– NOT Gate
A
A
– AND Gate
A
A•B
B
– OR Gate
A
B
Output
A+B
Input
Data always flows
in a unidirectional
manner from
inputs to outputs of
the logic gates!
Commonly used Gates
• Other commonly used gates
– NAND
A
(A•B)
B
– NOR
A
(A+B)
B
– XOR
A
B
AB
The circle (or bubble) indicates inversion
or NOT operation. You may add this
circle (or bubble) at the output or input of
any gate!
Equations to Circuits
• Convert Boolean equations to Logic Circuits
• Logic circuits drawn on paper are often also called
Schematics
– Straightforward process
• Convert each operator to a Logic Gate
– Suitably connect inputs and output
• Pay attention to crossing lines versus connected lines
A
B
No relationship
• Label all
between A & B.
A
B
No relationship
inputs and
outputs
between A & B. This
is preferred!
A
A
These two lines/wires
are the same!
Example 1
• A•B•C•D
– (A•B)•(C•D)
A
There are a few aspects to consider when using
the shortcut version:
1. All gates must be the same
2. Input to output transformation must be
straightforward
A•B
A•B•C•D
B
C
D
A
B
C
D
A•B•C•D
C•D
Standard Version (With 2-input Gates)
Shortcut Version (n-Input Gates)
Example 2
• Convert English to logic circuit
– Output O is
• A, if C=1
• B, if C=0
• Solution
– O = (A•C)+(B•C)
A
C
A•C
O=(A•C)+(B•C)
B
B•C
Shortcut for NOT
operation.
Design & Verification
• The graphical representation of logic circuits is called
a schematic.
• These days schematics are developed and verified
using software
– Modern software provide “virtual” components for
developing schematics
• Components include logic gates, ICs, and other electronic devices
including both digital and analog devices
– Software ease interconnection between components
– Logic circuits are verified using simulation
• There is a lot that goes into the simulations and it is an active area
of research and development.
• There are a wide variety of schematic software
available from various companies
– In this course we will use a software packaged called
MultiSIM from National Instruments Inc.
MultiSIM
• MultiSIM
– Feature roundup:
• Is a popular, industry standard, software from National
Instruments Inc.
• It is widely used for prototyping digital (and analog) circuits.
• The software provides many virtual components for developing
schematics
• Include simulation engine and graphical interface for verification
• Schematics can be used to directly synthesize Printed Circuit
Boards (PCBs) for mounting the physical integrated circuits and
devices.
– In this course we will be using MultiSIM to:
• Design logic circuits
• Verify their correct operation through simulation.
– The process will enable you to obtain a good understanding of logic
circuits and their operational characteristics.
– Note that MultiSIM is installed on all SEAS computers.
• But SEAS does not have student licenses for the software
Starting MultiSIM
• Start MultiSIM via the Windows menu options shown
below:
– Start→ EAS Applications → Engineering Apps →
MultiSIM 9 → MultiSIM 9
• It does take about 10-15 seconds for the software to startup (and
it looks like nothing is happening)
Using MultiSIM
Click the “Misc Digital” icon
to select a logic gate to be placed.
(All of these buttons pretty much take you to the
same set of options)
Use these buttons to
Start/Stop the simulation or
pause it after you have
completed design of a
schematic.
This area (with a grid) is where you
will develop your schematics.
Selecting Component to Place
On clicking this icon you will be
presented in the dialog box shown
below. Select component to place on
your schematic from this dialog box.
Preview of the
component is
shown here.
Choose appropriate “Group” and
“Family” settings to view
corresponding subset of components
in the adjacent “Component:” menu
Choose appropriate “Component” to
place in schematic from this list and
then click the
button.
Placing & Connecting Components
• To place a component in the schematic
– Selected a component as described in the previous
slide
• Refer to the ComponentList.doc file off Blackboard for a list
of commonly used components and their locations in
MultiSIM
– Press the
button
• The selected component will tag along with your mouse
cursor
• Click (left mouse button) at the appropriate location in the
schematic area (gridded area as shown below) to place a
component
Connecting Components
• Once you have placed two components on the
schematic you can connect pins of the components by
– However over a pin of a component
– The mouse cursor will turn into a cross hair
– Click on a pin and move the mouse to the next pin (or
wire) to connect components
• Don’t drag the mouse with the left-mouse-button depressed!
Release the mouse button and move the mouse
Simulation
• Once you have completed your schematic
– You must verify correct operation using
simulation
– Click simulate button (
) to start simulation
– You may toggle status of switches using
spacebar
– For dip switches you need to use number
(1,2,…,9) keys to toggle their status
General Selection Logic
• Develop a circuit to
select 1 of the given 5
inputs
– Let the inputs be A, B,
C, D, & E
– Assign unique
combinations of 1s and
0s to identify each Input
• Given n inputs you need k
bits such that 2k>=n
• In this case n=5 and
therefore k=3
• Let selection variables be
s1, s2, and s3
S1
S2
S3
O
0
0
0
A
0
0
1
B
0
1
0
C
0
1
1
D
1
0
0
E
General Selection (Cont.)
• Boolean equation for the example:
– O=(A•S1•S2•S3)+(B•S1•S2•S3)+(C•S1•S2•S3)+(D•S1•S2•S3)
+(E•S1•S2•S3)
S1
0
0
0
0
1
S2
0
0
1
1
0
S3
0
1
0
1
0
O
A
B
C
D
E
Logic Circuit for Selector
A
B
C
D
E
S1
S2
S3
O
Multiplexer (Mux)
• Select 1 given N circuits are
called Multiplexers
– Have N inputs
– K selection lines
– 1 output line
>= N
NxK
N inputs
•••
• Such that
2k
Multiplexer
•••
K select
lines
De-Multiplexer (DeMux)
• Move 1 input bit to selected output line
– 1 Input
– N Output lines
– K selection lines
• Such that
2K>=N
K select
lines
•••
1 Input
De-Multiplexer
•••
NxK
N Outputs
De-Multiplexer Logic Circuit
• 1 X 4 De-Multiplexer
A•S1•S2
A•S1•S2
A•S1•S2
A•S1•S2
A
S1
S2