Lecture Digital logic design - Lecture 31: PLAs and Arithmetic Logic Unit (ALU)

The following will be discussed in this chapter: Programmable logic array, K-map minimization, PLA minimizatio, main computation unit in most computer systems, ALUs perform a variety of different functions, individual chips can be chained together to make larger ALUs, build a data and control path.

Lecture 31 PLAs and Arithmetic Logic Unit (ALU)

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

° 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.

° The left part of the

diagram replaces the

decoder used in a

ROM.

° Connections can be

made in the “AND

array” to produce four

OR array

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.

PLA minimizatio

° For a PLA, we should minimize the number of

product terms for all functions together.

° We could express V 2 , V 1 and V 0 with just four total

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.

w

° 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

Arithmetic Logic Unit

° 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)

DataOut

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

Adder Subtract

AND

…

ALU Integrated Circuit

° Integrated circuit – off-the-shelf components

° Examine the functionality of this ALU chip

Performs 8 functions

° Change the select code to 101 and repeat.

• Function code indicates OR

° 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

Otherwise Out open-circuit

Load Clk

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

Using a Datapath

° Consider the following computation steps

1 ADD A, B and put result in A

2 Subtract A, B and put result in B

3 OR A, B put result in A

• Repeat starting from step 1

Determine values for Function, LoadA, LoadB

Function

LoadA

ALU

Modeling Control as a State

Machine

° Consider the following computation steps

1 ADD A, B and put result in A

2 Subtract A, B and put result in B

3 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

Modeling Control as a State

Machine

° Consider the following computation steps

1 ADD A, B and put result in A

2 Subtract A, B and put result in B

3 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?

Present State Next State Function LoadA LoadB

Function, LoadA, LoadB

Note: No minimization!

One line in ROM for each state

Putting the Control and Datapath

Possible to implement different functions!

Program the RAM to perform different sequences

Looks like software!

• 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

23

DLD Simulators

° Circuit Maker 2000

° MultiSim

° Electronic Workbench

CircuitMaker Workspace

° 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

Anatomy of a Schematic Drawing

Schematic, including device symbols, label-values and designations, wires, and pin dots

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

CktMaker Toolbar

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

3 Position the transistor at about mid-screen and then click the left mouse button once.

Placing the Resistors

The next procedure involves placing two resistors.

1 Select a Resistor [Passive

Components/Resistors/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 Don’t worry about the value yet.

4 Place a second resistor directly above the transistor This

is resistor R2.

Placing +V and Ground Devices

Now you.’ll place a voltage

source and change its

settings.

1Select a +V

[.General/Sources/+V] (1) by

pressing the 1 (number one)

Hotkey Place it above

resistor R2.

2Select 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

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

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.

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 > 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

Demo with examples