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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.


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.


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

where we get a research paper on Nano chemistry....?
Maira Reply
what are the products of Nano chemistry?
Maira Reply
There are lots of products of nano chemistry... Like nano coatings.....carbon fiber.. And lots of others..
Even nanotechnology is pretty much all about chemistry... Its the chemistry on quantum or atomic level
no nanotechnology is also a part of physics and maths it requires angle formulas and some pressure regarding concepts
Preparation and Applications of Nanomaterial for Drug Delivery
Hafiz Reply
Application of nanotechnology in medicine
what is variations in raman spectra for nanomaterials
Jyoti Reply
I only see partial conversation and what's the question here!
Crow Reply
what about nanotechnology for water purification
RAW Reply
please someone correct me if I'm wrong but I think one can use nanoparticles, specially silver nanoparticles for water treatment.
yes that's correct
I think
Nasa has use it in the 60's, copper as water purification in the moon travel.
nanocopper obvius
what is the stm
Brian Reply
is there industrial application of fullrenes. What is the method to prepare fullrene on large scale.?
industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
How we are making nano material?
what is a peer
What is meant by 'nano scale'?
What is STMs full form?
scanning tunneling microscope
how nano science is used for hydrophobicity
Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
what is differents between GO and RGO?
what is simplest way to understand the applications of nano robots used to detect the cancer affected cell of human body.? How this robot is carried to required site of body cell.? what will be the carrier material and how can be detected that correct delivery of drug is done Rafiq
analytical skills graphene is prepared to kill any type viruses .
Any one who tell me about Preparation and application of Nanomaterial for drug Delivery
what is Nano technology ?
Bob Reply
write examples of Nano molecule?
The nanotechnology is as new science, to scale nanometric
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Is there any normative that regulates the use of silver nanoparticles?
Damian Reply
what king of growth are you checking .?
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
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
what school?
biomolecules are e building blocks of every organics and inorganic materials.
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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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