Combinational Circuit Design

Combinational Circuit Logic circuits for digital systems may be combinational or sequential. A combinational circuit consists of logic gates whose outputs at any time are determined by combining the values of the applied inputs using logic operations. A combinational circuit performs an operation that can be specified logically by a set of Boolean expression. In addition to using logic gates, sequential circuits employ elements that store bit values. Sequential circuit outputs are a function of inputs and the bit value in storage elements. These values, in turn, are a function of previously applied inputs and stored values. As a consequence, the outputs of a sequential circuit depend not only on the presently applied values of the inputs, but also on pas inputs, and the behavior of the circuit must be specified by a sequence in time of inputs and internal stored bit values. A combinational circuit consists of input variables, output variables, logic gates and interconnections. The interconnected logic gates accept signals from the inputs and generate signals at the output. The n input variables come from the environment of the circuit, and the m output variables are available for use by the environment. Each input and output variable exists physically as a binary signal that represents logic 1 or logic 0.

For n input variables, there are 2^n possible binary input combinations. For each binary combination of the input variables, there is one possible binary value on each output. Thus, a combinational circuit can be specified by a truth table that lists the output values for each combination of the input variables. A combinational circuit can also be described by m Boolean function, one for each output variable. Each such function is expressed as function of the n input variables.

Combinational Circuit Design

The design of combinational circuit starts from a specification of the problem and culminates in a logic diagram or set of Boolean equations from which the logic diagram can be obtained. The procedure involves the following steps:

1. From the specifications of the circuit, determine the required number of inputs and outputs, and assign a letter symbol to each.

2. Derive the truth table that defines the required relation ship between inputs and outputs.

3. Obtain the simplified Boolean functions of each outputs as function of the input variables.

4. Draw the logic diagram.

5. Verify the correctness of the design.

I am a freelance content writer and currently attached with http://www.articles-heaven.com/ I am running http://www.superdiscountshop.com/ and http://www.pakreseller.com/

Sequential Circuit Design

Sequential Circuit
The digital circuits considered thus far have been combinational. Although every digital system is likely to include a combinational circuit, most systems encountered in practice also include storage elements, requiring that the systems be described as sequential circuits.

A combinational circuit and storage elements are interconnected to form a sequential circuit. The storage elements are circuits that are capable of storing binary information. The binary information stored in these elements at any given time defines the state of the sequential circuit at that time. The sequential circuit receives binary information from its environment via inputs. These inputs together with the present state of the storage elements, determine the binary value of the outputs. They also determine the values used to specify the next state of the storage elements. The next state of the storage elements is also a function of the inputs and present state. Thus, a sequential circuit is specified by a time sequence of inputs, internal states, and outputs.

Sequential Circuit Design
The design of clocked sequential circuits starts from a set of specification and culminates in a logic diagram or a list of Boolean functions from which the logic diagram can be obtained. In contrast to a combinational circuit, which is fully specified by a truth table, a sequential circuit requires a state table for its specification. Thus, the first step in the design of a sequential circuit is to obtain a state table or an equivalent representation such as state diagram.

A synchronous sequential circuit is made up of flip-flops and combinational gates. The design of the circuit consists of choosing the flip-flops and finding a combinational circuit structure which, together with the flip flops, produces a circuit that fulfills the stated specifications. The number of flip-flops is determined from the number of states in the circuit; n flip-flops can represent up to 2^n binary states. The combinational circuit is derived from the state table by evaluating the flip-flop input equations and output equations. In fact, once the type and number of flip-flops are determined, the design process involves a transformation from a sequential circuit problem into a combinational circuit problem. In this way, the techniques of combinational circuit design can be applied.

Design Procedure
This following is a procedure for the design of sequential circuits
1. Obtain either the state diagram or the state table from the statement of the problem.
2. If only a state diagram is available from step 1, obtain the state table.
3. Assign binary codes to the states.
4. Derive the flip-flops input equations from the next-state entries in the encoded state table.
5. Derive output equations from the output entries in the state table.
6. Simplify the flip-flops input equations and output equation.
7. Draw the logic diagram with D flip-flops and combinational gates, as specified by the flip-flop input equation and output equation.

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Reverse-Engineering Your Future

There are many ways of creating new methods and strategies for doing things well. One form of innovation is to take a powerful strategy from one area and apply it usefully in a completely different one. In that spirit, I have borrowed a concept from the field of engineering and will present you with several ways in which it can be used to plan and create a better future.

That concept is ‘reverse engineering’. Normally when a person engineers something, they start with a purpose, a need or a problem and create something which embodies that purpose, satisfies that need or solves the problem.

Reverse engineering is essentially the opposite process. You start out with the finished product and go backwards, retracing the creative method to find out how it works.

This is what happens when a company like Sony produces a new gadget. A competitor buys one and takes a screwdriver to it, taking it apart in order to find out the principles behind how it works. Then they can produce their own version built on similar principles.

Suppose you were to apply this process to one of your current goals. Assume the goal is complete at some point in the future and reverse engineer the pathway to that successful accomplishment. Here are three ways of doing the ‘reverse engineering’ process.

1) The Magic Pill Scenario

I’m not sure where this method originates, though I often use it with coaching clients to get past a problem.

It involves a simple question and some imagination.

The question is this:

"If I were to give you a magic pill that meant you would wake up tomorrow with the problem completely solved, what would have changed?"

This enables them to start thinking about the problem as solvable. This also presupposes that there is a solution and that it’s possible for them to get past their current obstacle.

They are then free to discover for themselves what changes they need to make. All we have to do after that is agree on how to make those changes, set up resources and a timeframe.

Then they are completely free to move into action, knowing they are going in the right direction in an acceptable timeframe.

2) Timeline method

Imagine that your future is stretched out in front of you on a line, where days, weeks, months and years are arranged in order. One day follows another. This is a representation of your timeline - your inner sense of time. Your mind uses your timeline to plan and schedule. It’s a bit like a ‘mental diary’ or planner.

First, assume that at some point in time, you will reach your goal.

Then move forward along that timeline until you get to a point in your future where the goal is accomplished.

At this point, check that it happens in a way that you’re happy with. If it’s not okay, change it until you’re completely happy with it.

Now turn around and look back along the timeline, noticing all of the events that took place before your goal - those actions which allowed you to accomplish your goal.

Be aware of what you did each step of the way. Your mind will fill in the details as you go.

Now you know how you will get there and have a complete plan.

To make this even better, look at your new plan. Are there any distractions or unnecessary steps involved? Use your awareness of this to streamline the plan further until it is at its best.

Write down the plan and move in to action!

(For more about this method, refer to my NLP Primer on timelines)

3) The Chunkwise Method

Henry Ford once said: "Nothing is particularly hard if you divide it into small jobs". He went on to prove his statement by working out all of the jobs involved in building a car and putting that knowledge to practical use. The result was the world’s first mass-produced car.

You can apply this process by breaking your goal down into a number of pieces, then subdividing those into smaller tasks. Then all you need to do to make that knowledge into a plan is to apply the three ‘power questions’.

I’ve detailed the full process below, using "creating a new ebook" as an example.

1 - Identify your goal
Example: creating a new ebook

2 - What are the major pieces needed or stages involved? (3-5 pieces)
Example: Research, Design, Writing the detailed text.

3 - what are the major pieces of each of those?
Example: Research - (Market research, Topic research)

4 - Apply three power questions to each piece :
Example: Topic research segment

A - How do you accomplish this piece?
Search internet, read relevant books, conduct studies in real world

B - How long will it take?
3 months

C - What order does this come in the bigger scheme?
After market research and before the design phase

Of course, you would go through all of the steps for each piece of every stage until you had a complete and comprehensive plan. Then you can decide if the time and effort involved are worth it. If not, you can work at ways of minimising the time taken in certain steps or do other steps in a more enjoyable or appealing way.

As a consequence of using the metaphor of reverse engineering, several strengths are revealed.

The process presupposes that the aim is possible and achievable, so we instantly bypass any doubts that could have stalled creative thoughts about a solution. If it’s really not possible, you’ll find out in the process.

You get to decide whether it’s worth it, which you can only assess fully if you know the full process involved in getting there. After all, it’s important to enjoy the journey as much as the final outcome.

You need to envision the outcome fully before you start, so you can adjust it and decide if you really want it that way. Needless to say, this saves a lot of time and effort.

Also bear in mind that none of these processes need to take very long - it’s all about finding a clear and acceptable path to your goal.

I hope these strategies are helpful in allowing you to decide on the great things you want in your future - and making them happen!

Philip Callaghan is an NLP Trainer and Coach who has been working full time with private clients for several years. He is a Licensed Master Practitioner and Trainer of Neuro Linguistic Programming (NLP) and a member of the International Association of Coaches.

Visit Phil's website http://www.resourcefulchange.co.uk for further articles.

Learn NLP with Phil at http://www.bronze-dragon.com/index.shtml

Reverse-Engineering Your Future

There are many ways of creating new methods and strategies for doing things well. One form of innovation is to take a powerful strategy from one area and apply it usefully in a completely different one. In that spirit, I have borrowed a concept from the field of engineering and will present you with several ways in which it can be used to plan and create a better future.

That concept is ‘reverse engineering’. Normally when a person engineers something, they start with a purpose, a need or a problem and create something which embodies that purpose, satisfies that need or solves the problem.

Reverse engineering is essentially the opposite process. You start out with the finished product and go backwards, retracing the creative method to find out how it works.

This is what happens when a company like Sony produces a new gadget. A competitor buys one and takes a screwdriver to it, taking it apart in order to find out the principles behind how it works. Then they can produce their own version built on similar principles.

Suppose you were to apply this process to one of your current goals. Assume the goal is complete at some point in the future and reverse engineer the pathway to that successful accomplishment. Here are three ways of doing the ‘reverse engineering’ process.

1) The Magic Pill Scenario

I’m not sure where this method originates, though I often use it with coaching clients to get past a problem.

It involves a simple question and some imagination.

The question is this:

"If I were to give you a magic pill that meant you would wake up tomorrow with the problem completely solved, what would have changed?"

This enables them to start thinking about the problem as solvable. This also presupposes that there is a solution and that it’s possible for them to get past their current obstacle.

They are then free to discover for themselves what changes they need to make. All we have to do after that is agree on how to make those changes, set up resources and a timeframe.

Then they are completely free to move into action, knowing they are going in the right direction in an acceptable timeframe.

2) Timeline method

Imagine that your future is stretched out in front of you on a line, where days, weeks, months and years are arranged in order. One day follows another. This is a representation of your timeline - your inner sense of time. Your mind uses your timeline to plan and schedule. It’s a bit like a ‘mental diary’ or planner.

First, assume that at some point in time, you will reach your goal.

Then move forward along that timeline until you get to a point in your future where the goal is accomplished.

At this point, check that it happens in a way that you’re happy with. If it’s not okay, change it until you’re completely happy with it.

Now turn around and look back along the timeline, noticing all of the events that took place before your goal - those actions which allowed you to accomplish your goal.

Be aware of what you did each step of the way. Your mind will fill in the details as you go.

Now you know how you will get there and have a complete plan.

To make this even better, look at your new plan. Are there any distractions or unnecessary steps involved? Use your awareness of this to streamline the plan further until it is at its best.

Write down the plan and move in to action!

(For more about this method, refer to my NLP Primer on timelines)

3) The Chunkwise Method

Henry Ford once said: "Nothing is particularly hard if you divide it into small jobs". He went on to prove his statement by working out all of the jobs involved in building a car and putting that knowledge to practical use. The result was the world’s first mass-produced car.

You can apply this process by breaking your goal down into a number of pieces, then subdividing those into smaller tasks. Then all you need to do to make that knowledge into a plan is to apply the three ‘power questions’.

I’ve detailed the full process below, using "creating a new ebook" as an example.

1 - Identify your goal
Example: creating a new ebook

2 - What are the major pieces needed or stages involved? (3-5 pieces)
Example: Research, Design, Writing the detailed text.

3 - what are the major pieces of each of those?
Example: Research - (Market research, Topic research)

4 - Apply three power questions to each piece :
Example: Topic research segment

A - How do you accomplish this piece?
Search internet, read relevant books, conduct studies in real world

B - How long will it take?
3 months

C - What order does this come in the bigger scheme?
After market research and before the design phase

Of course, you would go through all of the steps for each piece of every stage until you had a complete and comprehensive plan. Then you can decide if the time and effort involved are worth it. If not, you can work at ways of minimising the time taken in certain steps or do other steps in a more enjoyable or appealing way.

As a consequence of using the metaphor of reverse engineering, several strengths are revealed.

The process presupposes that the aim is possible and achievable, so we instantly bypass any doubts that could have stalled creative thoughts about a solution. If it’s really not possible, you’ll find out in the process.

You get to decide whether it’s worth it, which you can only assess fully if you know the full process involved in getting there. After all, it’s important to enjoy the journey as much as the final outcome.

You need to envision the outcome fully before you start, so you can adjust it and decide if you really want it that way. Needless to say, this saves a lot of time and effort.

Also bear in mind that none of these processes need to take very long - it’s all about finding a clear and acceptable path to your goal.

I hope these strategies are helpful in allowing you to decide on the great things you want in your future - and making them happen!

Philip Callaghan is an NLP Trainer and Coach who has been working full time with private clients for several years. He is a Licensed Master Practitioner and Trainer of Neuro Linguistic Programming (NLP) and a member of the International Association of Coaches.

Visit Phil's website http://www.resourcefulchange.co.uk for further articles.

Learn NLP with Phil at http://www.bronze-dragon.com/index.shtml

Laser Marking of ECC 200 2D Matrix Codes on Printed Circuit Boards

Manufacturers of electronic devices, from home audio equipment to automotive keyless entry systems, are increasingly seeking a reliable, cost effective method for uniquely identifying and tracking products through the manufacturing cycle, sales distribution and after-sale warranty verification. An autonomous, automated tracking system requires that a permanent, machine-readable code be applied to an internal printed circuit board to uniquely identify each product. The code must be durable enough to survive manufacturing processes including wave solder and board cleaning, must not affect circuit performance, and must store information in the small space available on real-estate conscious printed circuit boards.

The 2D matrix code provides a means to store alphanumeric character strings in very small areas of the printed circuit board. Laser marking technology provides a method for permanently applying 2D matrix codes to most board substrates. The high-resolution and high-accuracy of beam-steered laser marking systems provides the means to create well defined, high reliability codes regardless of code size. Laser marking also provides the user with a computer-controlled marking process for easy implementation into automated product tracking systems.

ECC 200 2D Matrix Codes

Two-dimensional symbologies encode information in the form of a checkerboard pattern of on/off cells. Specific advantages of Data Matrix codes over conventional 1D barcodes include:

· Encode information digitally, as opposed to the analog encoding of data in conventional barcodes.

· Can accommodate low-contrast printing directly on parts without requiring a label

· Offer very high information density - the highest among other common 2D codes, which means that you can place a lot of information in a very small area.

· They are scaleable, which means that you can print them and read them in various levels of magnification - only limited by the resolution of the available printing and imaging techniques.

· Due to the high information density inherent to Data Matrix codes, they also offer built-in error-correction techniques which allow fully recovering the message encoded in a Data Matrix symbol even if the mark is damaged and missing as much as 20% of the symbol.

· They are read by video cameras as opposed to a scanned laser beam used for reading conventional barcodes, which means that they can be read in any orientation.

ECC 200 Data Matrix is the most popular 2-D symbology with extensive use in automotive, aerospace, electronics, semiconductor, medical devices and other manufacturing unit-level traceability applications. Data Matrix codes are typically not replacing conventional linear barcodes, but are being used where traditional barcodes were too large, did not provide sufficient storage capacity, or were unreadable.

Data Matrix Code Structure

The 2D matrix codes appear as a "checkerboard" with the individual squares (cells) in either on on (white) or off (black) state. The code consists of four distinct elements.

· The Finder "L" Pattern consists of a solid row of cells along the left edge and bottom of the code that orients the reader to the layout of the 2D code.

· The Clock Track is a sequence of on/off cells along the right edge and top of the code that designates the row/column count to the reader.

· The Data Region is the pattern of black and white cells within the L pattern and the clock tracks that contain the alphanumeric content of the code.

· The Quiet Zone around the code must be free of any features that may be visible to the reader. The quiet zone should be at least two rows/columns wide for codes constructed of square cells. The quiet zone should be at least four rows/columns wide for codes constructed of circular cells (dots).

ECC 200 Data Matrix codes can store up to 3,116 numeric, 2,335 alphanumeric characters or 1,555 bytes of binary information in a 144 column by 144 row array. More realistic symbol dimensions for printed circuit boards can still contain a significant amount of information.

Laser Marking System

The laser marking system consists of the laser source, the beam-shaping optics, and the beam-steering system.

The laser is a light amplifier generating a bright, collimated beam of light at a specific wavelength. For FR4 and solder mask applications, most users choose the air-cooled CO2 laser operating at the 10,640nm far-infrared wavelength. This laser offers several performance and cost advantages, and produces excellent marking results.

The laser beam is projected through two beam-deflecting mirrors mounted to high-speed, high-accuracy galvanometers. As the mirrors are rotated under direction of the system computer, the laser beam scans across the target marking surface to "draw" the desired marking image.

After the laser beam is deflected from the beam-steering mirrors, it is focused to the smallest spot possible by flat-field focusing optics. The flat-field focusing assembly is a multi-element optical device designed to maintain the focal plane of the focused laser beam on a relatively flat plane throughout the marking field. The focused laser light significantly increases the power density and associated marking power.

The function of the laser optical train is to focus the laser beam to a small spot and to scan the laser beam over the target surface with high speed and accuracy. With the CO2 laser configuration, the focused spot diameter and associated marking line width is about 0.0035" to 0.004". Man-readable text characters can be as small as 0.040" and 2D matrix codes can be constructed from individual features as small as a single 0.004" dot.

PCB Marking

To mark printed circuit boards, the heat generated by the laser beam thermally alters the surface of the board to create a contrasting, legible mark. The process does not require labels, stencils, punches or any other auxiliary hardware or consumable.

For printed circuit board applications, several different variations of this technique can be used for different board/coating materials and background conditions.

· Solder mask or other Conformal Coatings on FR4 Boards -

The laser beam can alter the texture of the coating, giving it a lighter contrasting appearance, or can completely remove the coating to expose the underlying substrate or copper ground plane.

· Uncoated FR4 -

The laser beam alters the texture of the surface of the FR4 producing a near white appearance.

· Silk-screened Ink Block -

For users who already silkscreen component identification or other fixed information on the boards, a silk-screened white ink block can function as a background to the 2D matrix code to optimize readability. This technique is particularly helpful when…

o The background color of the board is similar to the color of the laser mark.

o Underlying circuitry would obscure the marking image to code readers.

o The board material is not suitable for laser marking, such as ceramic substrates.

2D Matrix Code Verification

Verification of the legibility and content of the 2D matrix codes is an important step in the overall quality program. After marking of each circuit, the reader verifies the integrity of the mark before indexing the laser marking head to the next marking location. The reader retrieves the alphanumeric text string from the 2D code and compares it with the text string that was to be marked.

The reader also evaluates the legibility of the code based on a variety of parameters including foreground/background contrast, geometric accuracy (skew, squareness, etc.) and the dimensional accuracy of both the marked and unmarked cells. The 2D matrix codes are then categorized as passed (green), warned (yellow) or failed (red). For overall production efficiency, the laser system can be programmed to verify only a select few 2D codes on a panel, then to automatically switch to verifying every code if the code legibility falls below a specified level.

Today's readers do an excellent job reading lower contrast 2D codes. If the laser marking system is installed on an assembly line with older 2D matrix readers downstream from the laser marker, the verification reader can be configured to evaluate the codes based on the performance of the older downstream readers to assure consistent performance throughout the assembly process.

Marking Performance

The typical printed circuit board marker is a fully automated, SMEMA-compliant, through-conveyor laser marking system. The overall productivity of the laser marker is comprised of several steps that make up the marking cycle. The steps required to mark one multi-array panel are…

1. Transport and positioning of the panel in the marking area.

2. Fiducial location detection (optional)

3. Marking of the first circuit in the array

4. Verification of the marked 2D matrix code (optional)

5. Motion of the laser marking head to the next circuit in the array.

6. Repeat steps 3 and 4 for the remaining circuits in the array.

7. Transport of the panel out of the laser marking system (synonymous with bringing the next panel in)

Cost of Operation

Cost of operation is much less than $1.00 per hour. Typical utilities requirements are 110VAC, 1-phase, 12A. A compressed air source is required for the pneumatics. Total utilities costs at maximum laser power (the laser should actually operate at less then 80% rated power) are $0.12 per hour. The primary consumable item is the CO2 laser tube that must be replaced every 3 to 5 years at a cost of typically $1,000.00 to $1,500.00. Assuming a 40-hour workweek and tube life of 3 years, the tube replacement cost would equate to $0.18 per hour for a total operating cost of $0.30 per hour under worst case conditions. Actual operating costs will be lower due to less than maximum electrical usage and longer tube life.

For typical pcb laser marking applications, the cost for marking is less than $0.0003 per circuit.

Summary

The electronics industry has been searching for a cost and technically effective means of applying machine-readable codes to printed circuit boards since the 1980's. Early attempts included laser marking linear barcodes on the board edge, a daunting challenge for reader alignment, and marking linear barcodes next to circuit traces, also a challenge for barcode readers. Barcode content was limited to a few characters due to limited space and the barcodes character-per-inch capacity.

The development of the 2D matrix code combined with the resolution, permanence and speed of beam-steered laser marking technology now offers manufacturers a reliable, cost-effective, flexible and verifiable means to uniquely identify every product through production, distribution and after-sale.

Visit Laser Marking or call (407) 679-9716

Richard Stevenson is the Sales Director for Control Micro Systems, Inc. a manufacturer of beam-steered laser marking systems. He has held numerous engineering, sales and marketing positions since joining the laser industry in 1976. He has published and presented numerous technical papers and articles on laser marking in trade publications and conferences and has represented the laser marking industry on the Laser Systems Product Group of the Association of Manufacturing Technology.

How To Clean Gel Flux Residue From a Circuit Board After Hand Soldering a Quad Flat Pack

This article describes how to clean gel flux residue from a circuit board after hand soldering a quad flat pack component. The process involves full immersion cleaning, which means fully submersing the board into solvent while brushing in order to dislodge and dissolve as much of the flux residue as possible.

Start by putting on some "powder free latex gloves" to protect your hands. Also make sure that you are wearing safety glasses and that your work area is reasonably well ventilated.

Place the board on the bench. No solvents are used at this stage. I call this step "dry wiping". Get a small brush, such as a horse hair or small parts cleaning brush and simply run the brush along each edge to remove the bulk of the flux residue.

Wipe the brush on a tissue to get the flux residue off of the brush. The objective is just to remove the bulk of the flux residue before the full immersion cleaning process.

Next, place your circuit board into a plastic container with some methylated spirits (or "metho").

The plastic container can be a lunch box, a food container or an empty ice cream container. Choose the size of the container depending on how big your circuit boards are and how many you want to put in to wash or soak at one time.

Ensure that there is enough metho in the container to fully immerse the board, including the components.

Then simply brush around the edge of the chip where the flux residue is. Continue to brush around until it looks like most of the flux residue has come off.

Take the board out of the metho to get an idea of how you are going.

Blow off the metho with compressed air (a nozzle, moisture separator, air hose and air compressor). The compressed air also helps to dislodge the residue, especially some of the residue sitting behind the chip legs.

At this stage you will be able to see how much of the flux residue is left on the board. Put the board back into the metho and do some more brushing.

Take the board out again and blow off the metho and residue with the compressed air. Again, you will be able to see how much residue is left. The residue will look like a think sticky film. Put the board back in and give it another go.

Keep going until you are satisfied that you have removed as much of the flux residue as possible. You don't have to worry is there is a little bit of flux residue left on the board because the gel flux used is "no-clean" type, which is inert and non-corrosive.

That completes this article. We covered how to clean gel flux residue from a circuit board, including "dry brushing", full immersion cleaning, using compressed air to blow off solvent and dislodge residue, and inspection.

There are many low cost tools and techniques for soldering small batches of printed circuit boards or one-off prototypes. Some of these techniques are well known while others have been invented and reinvented by small tech companies and advanced hobbyists. A few good tips can be worth their weight in gold (not just their weight in solder). Discover the tips that can save you days of soldering time or thousands of dollars in outsourcing costs. Anthony's site has many videos that reveal exactly these kinds of valuable soldering tips. Go to http://SuperSolderingSecrets.com

Combinational Circuit Design

Combinational Circuit Logic circuits for digital systems may be combinational or sequential. A combinational circuit consists of logic gates whose outputs at any time are determined by combining the values of the applied inputs using logic operations. A combinational circuit performs an operation that can be specified logically by a set of Boolean expression. In addition to using logic gates, sequential circuits employ elements that store bit values. Sequential circuit outputs are a function of inputs and the bit value in storage elements. These values, in turn, are a function of previously applied inputs and stored values. As a consequence, the outputs of a sequential circuit depend not only on the presently applied values of the inputs, but also on pas inputs, and the behavior of the circuit must be specified by a sequence in time of inputs and internal stored bit values. A combinational circuit consists of input variables, output variables, logic gates and interconnections. The interconnected logic gates accept signals from the inputs and generate signals at the output. The n input variables come from the environment of the circuit, and the m output variables are available for use by the environment. Each input and output variable exists physically as a binary signal that represents logic 1 or logic 0.

For n input variables, there are 2^n possible binary input combinations. For each binary combination of the input variables, there is one possible binary value on each output. Thus, a combinational circuit can be specified by a truth table that lists the output values for each combination of the input variables. A combinational circuit can also be described by m Boolean function, one for each output variable. Each such function is expressed as function of the n input variables.

Combinational Circuit Design

The design of combinational circuit starts from a specification of the problem and culminates in a logic diagram or set of Boolean equations from which the logic diagram can be obtained. The procedure involves the following steps:

1. From the specifications of the circuit, determine the required number of inputs and outputs, and assign a letter symbol to each.

2. Derive the truth table that defines the required relation ship between inputs and outputs.

3. Obtain the simplified Boolean functions of each outputs as function of the input variables.

4. Draw the logic diagram.

5. Verify the correctness of the design.

I am a freelance content writer and currently attached with http://www.articles-heaven.com/ I am running http://www.superdiscountshop.com/ and http://www.pakreseller.com/