Lecture 31 PLAs and Arithmetic Logic Unit (ALU)

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Lecture 31PLAs and Arithmetic Logic Unit (ALU)
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Programmable Logic Array

• A ROM is potentially inefficient because it uses
  a decoder, which generates all possible minterms.
  No circuit minimization is done.
• Using a ROM to implement an n-input function
  requires
• An n-to-2n decoder, with n inverters and 2n
  n-input AND gates.
• An OR gate with up to 2n inputs.
• The number of gates roughly doubles for each
  additional ROM input.
• A programmable logic array, or PLA, makes the
  decoder part of the ROM programmable too.
  Instead of generating all minterms, you can
  choose which products (not necessarily minterms)
  to generate.

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A blank 3 x 4 x 3 PLA

• This is a 3 x 4 x 3 PLA (3 inputs, up to 4
  product terms, and 3 outputs), ready to be
  programmed.
• The left part of the diagram replaces the decoder
  used in a ROM.
• Connections can be made in the AND array to
  produce four arbitrary products, instead of 8
  minterms as with a ROM.
• Those products can then be summed together in the
  OR array.

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K-map minimization

• The normal K-map approach is to minimize the
  number of product terms for each individual
  function.
• For our three functions, this would result in a
  total of six different product terms.

V2 V1 V0
V2 ?m(1,2,3,4) V1 ?m(2,6,7) V0 ?m(4,6,7)
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PLA minimizatio

• For a PLA, we should minimize the number of
  product terms for all functions together.
• We could express V2, V1 and V0 with just four
  total products

V2 xyz xz xyz V1 xyz xy V0
xyz xy
V2 ?m(1,2,3,4) V1 ?m(2,6,7) V0 ?m(4,6,7)
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PLA

• So we can implement these three functions using a
  3 x 4 x 3 PLA

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Summary

• ROMs provide stable storage for data
• ROMs have address inputs and data outputs
• ROMs directly implement truth tables
• ROMs can be used effectively in Mealy and Moore
  machines to implement combinational logic
• In normal use ROMs are read-only
• They are only read, not written
• ROMs are often used by computers to store
  critical information
• Unlike SRAM, they maintain their storage after
  the power is turned off
• ROMs and PLAs are programmable devices that can
  implement arbitrary functions, which is
  equivalent to acting as a read-only memory.
• ROMs are simpler to program, but contain more
  gates.
• PLAs use less hardware, but it requires some
  effort to minimize a set of functions. Also, the
  number of AND gates available can limit the
  number of expressible functions.

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Overview

• Main computation unit in most computer systems
• ALUs perform a variety of different functions
• Add, subtract, OR, AND
• Example ALU chip (74LS382)
• Has data and control inputs
• Individual chips can be chained together to make
  larger ALUs
• ALUs are important parts of datapaths
• ROMs often are used in the control path
• Build a data and control path

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Arithmetic Logic Unit
DataA
DataB

• Arithmetic logic unit functions
• Two multi-bit data inputs
• Function indicates action (e.g. add, subtract,
  OR)
• DataOut is same bit width as multi-bit inputs
  (DataA and DataB)
• ALU is combinational
• Conditions indicate special conditions of
  arithmetic activity (e.g. overflow).

Function
ALU
Conditions
DataOut
Think of ALU as a number of other arithmetic and
logic blocks in a single box! Function selects
the block

AND
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ALU Integrated Circuit

• Integrated circuit off-the-shelf components
• Examine the functionality of this ALU chip

Performs 8 functions
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Example

• Determine the 74HC382 ALU outputs for the
  following inputs S2S1S0010, A3A2A1A00100,
  B3B2B1B00001, and CN1.
• Function code indicates subtract
• 0100 0001 0011
• Change the select code to 101 and repeat.
• Function code indicates OR
• 0100 OR 0001 0101

Synchronize ALU with a clock
DataA
DataB
Function
ALU
Conditions
DataOut
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Expanding the ALU

• Multi-bit ALU created by connecting carry output
  of low-order chip to carry in of high order

Eight-bit ALU formed from 2 four-bit ALUs
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Datapath components

• Tri-state buffer
• Loadable register

If Enable asserted, Out In Otherwise
Out open-circuit
In
Out
Enable
Load
Clk
Data stored on rising edge if Load is asserted
(e.g. Load 1)
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Computation in a Typical Computer

• Control logic often implemented as a finite state
  machine (including ROMs)
• Datapath contains blocks such as ALUs, registers,
  tri-state buffers, and RAMs
• In a processor chip often a 5 to 1 ratio of
  datapath to control logic

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Using a Datapath

• Consider the following computation steps
• ADD A, B and put result in A
• Subtract A, B and put result in B
• OR A, B put result in A
• Repeat starting from step 1

Determine values for Function, LoadA, LoadB
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Modeling Control as a State Machine

• Consider the following computation steps
• ADD A, B and put result in A
• Subtract A, B and put result in B
• OR A, B put result in A
• Repeat starting from step 1

Determine values for Function, LoadA, LoadB
Model control as a state machine. Determine
control outputs for each state
S0
S1
S2
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Modeling Control as a State Machine

• Consider the following computation steps
• ADD A, B and put result in A
• Subtract A, B and put result in B
• OR A, B put result in A
• Repeat starting from step 1

States S0 00 S1 01 S2 10
Present State Next State Function
LoadA LoadB 00
01 011 1
0 01 10
010 0 1
10 00
101 1 0
We know how to implement this using an SOP. Can
we use a ROM?
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ROM Implementation of State Machine
Present State Next State Function
LoadA LoadB 00
01 011 1
0 01 10
010 0 1
10 00
101 1 0
States S0 00 S1 01 S2 10
Note No minimization! One line in ROM for each
state
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Putting the Control and Datapath Together
ROM
00
0101110
01
1001001
10
0010110
PS
NS
LoadA
A
B
LoadB
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Function
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What if we replaced the ROM with RAM?
RAM
00
Looks like software!
0101110
01
1001001
10
0010110
PS
NS
LoadA
A
B
LoadB
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Function
Possible to implement different
functions! Program the RAM to perform different
sequences
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Summary

• ALU circuit can perform many functions
• Combinational circuit
• ALU chips can be combined together to form larger
  ALU chips
• Remember to connect carry out to carry in
• ALUs form the basis of datapaths
• ROMs can form the basis of control paths
• Combine the two together to build a computing
  circuit

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DLD Simulators

• Circuit Maker 2000
• MultiSim
• Electronic Workbench

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CircuitMaker Workspace
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Connectivity

• An important feature of CircuitMaker is the way
  electrical connections between the elements in
  your design are recognized.
• The concept of connectivity is the key to using
  CircuitMaker to draw and simulate electronic
  circuits. The program stores connection
  information for simulation, and it is also used
  for creating and exporting netlists into
  TraxMaker or other pcb layout programs to create
  a working printed circuit board (PCB).
• CircuitMaker sections
• Schematic Window
• Analysis Window
• Panel
• Schematic window is where the schematics are
  drawn. One circuit file at a time can be opened
  into this window
• Analysis Window is where the simulation results
  are
• Panel has tabs across the top which are used to
  select controls which are relevant to the
  available displayed

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Anatomy of a Schematic Drawing
Schematic, including device symbols,
label-values and designations, wires, and pin dots
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CktMaker Conventions

• .CKT Schematic (or Circuit) files
• .DAT Data files (Hotkeys device library
  classifications)
• .LIB Device library files
• .MOD Model files
• .SUB Subcircuit files
• .SDF Waveform display setup files

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CktMaker Toolbar
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Drawing a Schematic

• Using the Browse tab in the Panel
• Selecting a transistor
• Selecting resistors
• Selecting a V and ground device
• Changing resistor and transistor label values
• Wiring the circuit

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Placing a Transistor

• Begin the circuit by selecting the 2N2222A
  transistor .General/BJTs/NPN Trans.
• 1 Select .General / BJTs / NPN TransC in the
  Browse tree. Select the 2N2222A transistor in
  the Model list.
• 2 Click Place to select this device from the
  library. You can also click the Search tab on
  the Panel, type 2n2222a , and click Find to
  quickly find the part.
• 3 Position the transistor at about mid-screen
  and then click the left mouse button once.

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Placing the Resistors

• The next procedure involves placing two
  resistors.
• 1 Select a Resistor Passive Components/Resistor
  s/Resistor (r) by pressing the r Hotkey on the
  keyboard. Notice that the resistor is oriented
  horizontally and moves around the screen with the
  mouse.
• 2 Press the r key again (or click the Right
  mouse button) to rotate the device 90.
• 3 Drag the resistor above and to the left of the
  transistor and click the Left mouse button once
  to place it. This is resistor R1. Dont worry
  about the value yet.
• 4 Place a second resistor directly above the
  transistor. This is resistor R2.

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Placing V and Ground Devices

• Now you.ll place a voltage source and change its
  settings.
• Select a V .General/Sources/V (1) by
  pressing the 1 (number one) Hotkey. Place it
  above resistor R2.
• Select a Ground .General/Sources/Ground (0) by
  pressing the 0 (zero) Hotkey. Place it below the
  transistor.
• 3 Double-click the V device using the Left
  mouse button to open the Device Properties
  dialog box

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Placing V and Ground Devices

• 4 Change the Label-Value field to read 15V.
• 5 Click once on the topmost Visible check box.
  This causes the V name to be hidden on the
  schematic.
• 6 Click once on the third Visible check box from
  the top. This causes the V1 designation to be
  hidden on the schematic. Click OK.
• Changing Resistor Label-Values
• 1 Double-click resistor R1.
• 2 Change the Label-Value field to read 220k,
  then click OK.
• 3 Double-click resistor R2.
• 4 Change the Label-Value field to read 870k,
  then click OK.

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Wiring the Circuit Together

• 1 Select the Wire Tool from the Toolbar.
• 2 Place the cursor on the emitter pin of the
  transistor (the pin with the arrow.) When the
  cursor gets close to the pin, a small rectangle
  appears.
• 3 Click and hold the left mouse button, then
  drag the wire to the pin of the Ground symbol.
• 4 Release the mouse button to make the
  connection.
• 5 Place the cursor on the bottom pin of R2, and
  then click and hold the mouse button to start a
  new wire.
• 6 Drag the end of the wire to the collector pin
  of the transistor and release the mouse button.
• 7 Connect a wire from the top pin of R2 to 15V.
• 8 Connect another wire from the bottom pin of R1
  to the base of the transistor.
• 9 Finally, connect a wire from the top pin of R1
  to the middle of the wire which connects 15V to
  R2.

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Digital Logic Simulation

• 1 Click the Open button in the Toolbar.
• 2 Select the SIM.CKT file from the list of
  available circuits. The SIM.CKT circuit contains
  several mini-circuits and is useful for
  demonstrating CircuitMaker.s digital simulation
  features.
• 3 Click the Run button on the Toolbar to start
  simulation. You know that simulation is running
  when you see a Hex Display showing a count
  sequence.
• 4 Select the Probe Tool from the Toolbar and
  touch its tip to the wire just to the left of the
  label .Probe Wire to the Left.. The letter L
  will be displayed in the Probe Tool.
• 5 Move the tip of the Probe Tool to the Logic
  Switch labeled .Toggle Switch. and click near
  its center. The Logic Display connected to the
  output of this minicircuit should then start to
  toggle on and off rapidly.
• 6 Click the Horizontal Split button on the
  Toolbar to open the digital Waveforms window.
  Each node in the circuit that has a SCOPE device
  attached is charted in this window.
• 7 Select Simulation gt Active Probe, then run
  the simulation again. A new waveform called Probe
  displays in the Waveforms window. Watch what
  happens to this waveform as you move the Probe
  Tool around the circuit.
• 8 Click the Trace button in the Toolbar to see
  the state of every wire in the circuit as the
  state changes. A red wire indicates a high state,
  a blue wire indicates a low state.
• 9 Click the Pause button in the Toolbar to stop
  simulation.

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Demo with examples