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DSD_Chapter 2 explains how a ROM can be used as Boolean Function Generator.

Digital System Design_Chapter 2_Basic Philosophy of Simple Programmable Logic Devices(SPLD).

In Chapter 1_ Part 2 we saw that PLAs, PALs, GALs, PLDs and PROM are collectively called Simple Programmable Logic Devices. Here we will examine PLA, PAL and PROM closely to understand how exactly Sum of Products Boolean Function is achieved.

CODE CONVERTERS- DECODER&ENCODER.

All these programmable devices are based on the philosophy of M-bit Code Input being converted to N-bit Code output.

2 M = µ and 2 N = α.

Here α may be less than µ. In that case each of the M-bit code does not have a corresponding unique N-bit code. Many of the M-bit codes may have the same N-bit code.

How does the code converter work:

The figure 1 gives the code converter working.

Figure 1. Code-converter System.

ROM is typical Code Converter system.

Here M-bit decoder is AND system and N-bit encoder is OR system.

Therefore:

Each bit-line Yi = SUM of PRODUCT of X0,X1,X2…..X(m-1).

Decoder Word Line generates PRODUCT terms.

A DECODER is realized by Multiplexer also known as MUX. MUX is nothing but a combination of AND gates. In Figure 2 we show a 4-bit binary to decimal decoder:

Figure 2. 4-bit binary to decimal decoder.

Figure 3. Block Model of 4-bit binary to decimal decoder.

Table 1. Truth Table of the decoder

D C B A Word Line Decoded Decimal Value
0 0 0 0 W0 0
0 0 0 1 W1 1
0 0 1 0 W2 2
0 0 1 1 W3 3
0 1 0 0 W4 4
0 1 0 1 W5 5
0 1 1 0 W6 6
0 1 1 1 W7 7
1 0 0 0 W8 8
1 0 0 1 W9 9

In Figure 3, for every BCD code one of the 10 Word lines will go HIGH and the remaining lines will be LOW. Figure 2 tells us that every Word Line is a PRODUCT of 4 Variables A,B,C,D and their complements A′ , B′,C′,D′ .

Encoder Bit Line is SUM of Words.

Keyboard of a Computer generates 8-bit ASCII Code on pressing one of the keys. Hence Keyboard is ENCODER ARRAY. For simplicity of presentation we present 10Key - 4bit Encoder. The customer will have to decide and specify the 4-bit codes corresponding to 10 keys. That is the Customer will provide the Truth Table.

Suppose the customer provides the following Truth Table 2:

Table 2. The Truth Table of the Encoder.

W9 W8 W7 W6 W5 W4 W3 W2 W1 W0 Y3 Y2 Y1 Y0
0 0 0 0 0 0 0 0 0 1 0 0 0 0
0 0 0 0 0 0 0 0 1 0 0 0 0 1
0 0 0 0 0 0 0 1 0 0 0 0 1 0
0 0 0 0 0 0 1 0 0 0 0 0 1 1
0 0 0 0 0 1 0 0 0 0 0 1 0 0
0 0 0 0 1 0 0 0 0 0 0 1 0 1
0 0 0 1 0 0 0 0 0 0 0 1 1 0
0 0 1 0 0 0 0 0 0 0 0 1 1 1
0 1 0 0 0 0 0 0 0 0 1 0 0 0
1 0 0 0 0 0 0 0 0 0 1 0 0 1

Figure 4. 10 Key to 4-bit Encoder Array.

Here the Word line (rows) is crossing the bit-line.

If W1 is pressed, 5V is applied to the corresponding Word line or to the corresponding ROW. The Row crosses the four bit-lines at the four intersections. Which ever intersection is shorted on that bit line ‘1’ is generated as seen in Figure 4. Where intersections are not shorted there we get ‘0’ on the bit line. For W1, Y3=0,Y2=0,Y1=1, Y0 = 0 binary code is generated as desired by the customer.

For W6, 0-1-1-0 is generated. Now let us examine the bit lines:

Y0 is HIGH if W1 is pressed or W1 is HIGH or W3 is HIGH or W5 is HIGH or W7 is HIGH or W9 is HIGH.

Therefore Y0 = W1 + W3 + W5 + W7 + W9;

Similarly Y1 = W2 + W3 + W6 + W7;

Questions & Answers

what is Nano technology ?
Bob Reply
write examples of Nano molecule?
Bob
The nanotechnology is as new science, to scale nanometric
brayan
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Damian
Is there any normative that regulates the use of silver nanoparticles?
Damian Reply
what king of growth are you checking .?
Renato
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
Stoney Reply
why we need to study biomolecules, molecular biology in nanotechnology?
Adin Reply
?
Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
Adin
why?
Adin
what school?
Kyle
biomolecules are e building blocks of every organics and inorganic materials.
Joe
anyone know any internet site where one can find nanotechnology papers?
Damian Reply
research.net
kanaga
sciencedirect big data base
Ernesto
Introduction about quantum dots in nanotechnology
Praveena Reply
what does nano mean?
Anassong Reply
nano basically means 10^(-9). nanometer is a unit to measure length.
Bharti
do you think it's worthwhile in the long term to study the effects and possibilities of nanotechnology on viral treatment?
Damian Reply
absolutely yes
Daniel
how to know photocatalytic properties of tio2 nanoparticles...what to do now
Akash Reply
it is a goid question and i want to know the answer as well
Maciej
characteristics of micro business
Abigail
for teaching engĺish at school how nano technology help us
Anassong
Do somebody tell me a best nano engineering book for beginners?
s. Reply
there is no specific books for beginners but there is book called principle of nanotechnology
NANO
what is fullerene does it is used to make bukky balls
Devang Reply
are you nano engineer ?
s.
fullerene is a bucky ball aka Carbon 60 molecule. It was name by the architect Fuller. He design the geodesic dome. it resembles a soccer ball.
Tarell
what is the actual application of fullerenes nowadays?
Damian
That is a great question Damian. best way to answer that question is to Google it. there are hundreds of applications for buck minister fullerenes, from medical to aerospace. you can also find plenty of research papers that will give you great detail on the potential applications of fullerenes.
Tarell
what is the Synthesis, properties,and applications of carbon nano chemistry
Abhijith Reply
Mostly, they use nano carbon for electronics and for materials to be strengthened.
Virgil
is Bucky paper clear?
CYNTHIA
carbon nanotubes has various application in fuel cells membrane, current research on cancer drug,and in electronics MEMS and NEMS etc
NANO
so some one know about replacing silicon atom with phosphorous in semiconductors device?
s. Reply
Yeah, it is a pain to say the least. You basically have to heat the substarte up to around 1000 degrees celcius then pass phosphene gas over top of it, which is explosive and toxic by the way, under very low pressure.
Harper
Do you know which machine is used to that process?
s.
how to fabricate graphene ink ?
SUYASH Reply
for screen printed electrodes ?
SUYASH
What is lattice structure?
s. Reply
of graphene you mean?
Ebrahim
or in general
Ebrahim
in general
s.
Graphene has a hexagonal structure
tahir
On having this app for quite a bit time, Haven't realised there's a chat room in it.
Cied
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
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Source:  OpenStax, Digital system design using vhdl. OpenStax CNX. Apr 01, 2013 Download for free at http://cnx.org/content/col11213/1.8
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