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Introduction to Programmable Logic Devices
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Today, we will start our discussion on programmable logic devices, also known as PLDs. Can anyone tell me what a PLD is?
Isn't it a type of circuit that can be programmed to perform various logic functions?
Exactly! PLDs allow us to implement specific logical designs through programmable arrays. What do you think makes these devices useful?
They are flexible and can be modified for different projects without needing new hardware.
Good point! Flexibility is key. PLDs can be reprogrammed, which saves time and resources during development.
Let's remember that PLDs include variants like PLAs and PALs. Can anyone explain the difference?
PLAs have programmable AND and OR gates whereas PALs have programmable AND arrays and fixed OR gates.
Perfect! This brings us to their architectures, including how they process inputs and produce outputs.
Understanding Boolean Functions
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Next, letβs talk about how we simplify Boolean functions when using PLDs. Why do you think simplification is important?
It probably helps in reducing the number of logic gates needed, right?
Exactly! Fewer gates mean less complexity and lower costs. When using PLAs, all input variables are available at each AND gate, which allows for easier management of multiple inputs.
Do we always have to minimize the expressions first?
While simplification is ideal, in some cases like the full adder example, it may not reduce the number of gates required. Can anyone remember the sums and carry outputs for a full adder?
Yes! The sum is S and the carry-out is C from the truth table.
Great job! Understanding these components ensures effective design using PLDs.
Application and Examples
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Letβs look at specific examples of implementing functionalities with PLDs. Who can tell me about the function of a full adder?
A full adder sums two bits and a carry-in to produce a sum and carry-out.
Exactly! When we built a full adder using a PLA, we utilized multiple AND gates for the summed output. Can anyone explain how we represent that in truth tables?
We write down all possible inputs and corresponding outputs in a table format!
Correct! The truth table helps us visualize the relationships. Now letβs explore comparators, which determine equality or inequality between two numbers.
The comparators produce outputs like equal to, less than, or greater than, right?
Exactly, and we can design those using a similar method as with the full adder. Understanding these functions helps us grasp how PLDs can be used efficiently.
Comparing PLAs and PALs
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To wrap up, let's compare PLAs and PALs. What are some advantages of using PALs?
They have a fixed OR gate design, which simplifies the circuit and saves time for designs that donβt require complex configurations.
Exactly! Additionally, PALs tend to be faster since they don't have to reprogram the OR gates. How might the fixed architecture affect the outputs?
It could limit flexibility in some cases, but it's also more straightforward for many standard applications.
Well said! Balancing flexibility and simplicity is crucial in digital design, and understanding the distinctions helps in selecting the right device for the job.
Introduction & Overview
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Quick Overview
Standard
The section discusses programmable logic devices such as Programmable Logic Arrays (PLAs) and Programmable Array Logic (PALs). It explains their architectures, the importance of simplification in Boolean functions, and provides examples of implementing functions like full adders and comparators. It also touches upon the features and flexibility of PALs compared to PLAs.
Detailed
Programmable Logic Devices
Programmable Logic Devices (PLDs), including Programmable Logic Arrays (PLAs) and Programmable Array Logic (PALs), play a vital role in digital electronics by allowing for reconfigurable logic circuits.
Key Components of PLAs:
- PLAs consist of a programmable AND gate and a programmable OR gate arrays.
- Inputs are fed into the AND gates generating product terms, which are then configured at the OR gates to create desired logical outputs.
Simplification of Boolean Functions:
- When implementing Boolean functions, simplification reduces the number of product terms, minimizing the required AND gates. Each function should be restructured to use common product terms wherever possible, although with PLAs, the handling of multiple inputs at the AND gates provides more flexibility than in fixed architecture.
Examples:
- Example implementations, such as the design of a binary full adder using PLAs, demonstrate how logical expressions can be managed and implemented effectively.
- Comparators were also illustrated, revealing the different logical outputs for conditions like equality and inequality of two binary numbers.
PAL Architecture:
- Unlike PLAs, PALs feature a fixed OR gate array, providing simplifications when the product-term sharing is not needed.
- PALs offer features like registered outputs and programmable output polarities, expanding their usability in applications.
In brief, this section highlights the significance of PLDs in performing complex logic operations efficiently with ease of programmability.
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Understanding Programmable Logic Arrays (PLAs)
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While implementing a given Boolean function with a PLA, it is important that each expression is simplified to a minimum number of product terms which would minimize the number of AND gates required for the purpose. Since all input variables are available to different AND gates, simplification of Boolean functions to reduce the number of literals in various product terms is not important. In fact, each of the Boolean functions and their complements should be simplified. What is desirable is to have fewer product terms and product terms that are common to other functions. We recall that PLAs offer the flexibility of implementing Boolean functions in both AND-OR and AND-OR-INVERT forms.
Detailed Explanation
In this chunk, we are discussing how PLAs are utilized to implement Boolean functions. To be effective, one should simplify these functions to use the least number of product terms. While normally we would try to reduce the number of literals (the basic elements of a Boolean expression), in the case of PLAs, since all input variables can be accessed by the AND gates, this particular simplification is less critical. However, simplifying functions to have common product terms is beneficial because it can reduce redundancy when implementing multiple functions.
Examples & Analogies
Think of PLAs like chefs in a kitchen using a variety of ingredients (input variables). If we have a vast selection of ingredients available to all chefs (AND gates), we can focus on simplifying recipes (Boolean functions) to use fewer primary components (product terms) while still making delicious dishes (output functions) that complement each other.
Implementation Example: Full Adder
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Example 9.2 Show the logic arrangement of both a PROM and a PLA required to implement a binary full adder. Solution The truth table of a full adder is given in Table 9.1. The Boolean expressions for sum S and carry-out C can be written as follows: S = Ξ£m(1, 2, 4, 7) C = Ξ£m(3, 5, 6, 7). If we simplify the Boolean expressions for the sum and carry outputs, we will find that the expression for the sum output cannot be simplified any further, and also that the expression for carry-out can be simplified to three product terms with fewer literals. If we examine even the existing expressions, we find that we would need seven AND gates in the PLA implementation. And if we use the simplified expressions, even then we would require the same number of AND gates. Therefore, the simplification here would not help as far as its implementation with a PLA is concerned. Figure 9.15 shows the implementation of a full adder with a PLA device.
Detailed Explanation
In this example, we are tasked with designing a full adder using a Programmable Logic Array (PLA). A full adder is a circuit that computes the sum of three binary inputs: A, B, and Carry-in (Ci). The truth table for the full adder outlines the various combinations of inputs and their corresponding outputs. By deriving the Boolean equations for the Sum (S) and Carry-out (C), we see that even after simplifying these expressions, the number of AND gates needed remains unchangedβindicating that simplification may not always reduce component requirements. This practical aspect shows that while simplification is generally necessary for efficiency, it may not yield significant differences in some designs.
Examples & Analogies
Imagine trying to simplify a recipe that makes the same dish regardless of how many ingredients you use. You might think of using fewer ingredients to save on preparation time; however, you may find that you still need to keep the same amount of core components to achieve the same taste. Similarly, in the full adder example, despite the simplifications, we still require the same number of gates to produce the desired output.
Designing a Comparator Using a PLA
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Example 9.3 We have two two-bit binary numbers A1A0 and B1B0. Design a PLA device to implement a magnitude comparator to produce outputs for A being βequal toβ, βnot equal toβ, βless thanβ, and βgreater thanβ B. Solution The Boolean expressions for the desired outputs are given in the following equations for equal to, not equal to, less than, and greater than. We need to have a PLA device with 12 AND gates to meet the requirement. Also, since there are four outputs, we need to have four OR gates at the output.
Detailed Explanation
In this chunk, we are tasked with designing a magnitude comparator using a PLA to compare two binary numbers. The task specifies producing outputs that indicate whether the first number is equal to, not equal to, less than, or greater than the second number. To achieve this, we formulate Boolean expressions that define the logic for each comparison. After establishing the necessary logic functions, we determine that a PLA with 12 AND gates and 4 OR gates will suffice for this task, illustrating not only how to implement comparison logic but also the flexibility and capacity of PLAs in handling multiple output requirements.
Examples & Analogies
Consider two people comparing their heights. A comparator is like a judge who determines if one is taller (greater than), shorter (less than), or equal in height. In programming, just like comparing heights, a PLA can be set up to execute these logical comparisons, using various components (AND and OR gates) to derive a definitive answer based on the inputs.
Exploring Programmable Array Logic (PAL)
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The programmable array logic (PAL) device is a variant of the PLA device. It has a programmable AND gate array at the input and a fixed OR gate array at the output. The idea to have a fixed OR gate array at the output and make the device less complex originated from the fact that there were many applications where the product-term sharing capability of the PLA was not fully utilized and thus wasted. The PAL device is a trademark of Advanced Micro Devices Inc. PAL devices are however less flexible than PLA devices. The flexibility of a PAL device can be enhanced by having different output logic configurations.
Detailed Explanation
This chunk discusses the difference between PALs and PLAs. A PAL incorporates a programmable AND gate array at the input but features a fixed design for its OR gate array at the output. This simplification allows for efficiency in certain applications where the full flexibility of a PLA isn't necessary. Although PALs typically provide less versatility compared to PLAs, advancements such as various output configurations can enhance their functionality, making them suitable for a wider range of digital logic applications.
Examples & Analogies
If a PLA is like a full-service restaurant offering an extensive menu with every food item customizable, a PAL is like a fast-food restaurant with a set menu but known for speed and efficiency. Here, customers (engineers) appreciate the speed and straightforwardness of a PAL when their needs do not require the extensive options provided by a PLA.
Definitions & Key Concepts
Learn essential terms and foundational ideas that form the basis of the topic.
Key Concepts
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Programmable Logic Devices (PLDs): Digital circuits that can be programmed for multiple logic functions.
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Programmable Logic Arrays (PLAs): PLDs with programmable AND and OR gates.
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Programmable Array Logic (PAL): PLDs with programmable AND gates and fixed OR gates, providing increased speed and simplicity.
Examples & Real-Life Applications
See how the concepts apply in real-world scenarios to understand their practical implications.
Examples
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Example implementations, such as the design of a binary full adder using PLAs, demonstrate how logical expressions can be managed and implemented effectively.
-
Comparators were also illustrated, revealing the different logical outputs for conditions like equality and inequality of two binary numbers.
-
PAL Architecture:
-
Unlike PLAs, PALs feature a fixed OR gate array, providing simplifications when the product-term sharing is not needed.
-
PALs offer features like registered outputs and programmable output polarities, expanding their usability in applications.
-
In brief, this section highlights the significance of PLDs in performing complex logic operations efficiently with ease of programmability.
Memory Aids
Use mnemonics, acronyms, or visual cues to help remember key information more easily.
π΅ Rhymes Time
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PALs are fixed, but a flexible PLA, can change at will, night or day.
π Fascinating Stories
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Imagine a magician (PLA) who can create any spell (logic function) versus a juggler (PAL) who can only use set patterns but does them perfectly.
π§ Other Memory Gems
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Remember 'PAL' for 'PAs are Less flexible' compared to PLAs.
π― Super Acronyms
Using 'PLD' to remember 'Programmable Logic Device' makes it easy to define.
Flash Cards
Review key concepts with flashcards.
Glossary of Terms
Review the Definitions for terms.
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Term: Programmable Logic Device (PLD)
Definition:
A digital device that can be programmed to implement specific logic functions.
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Term: Programmable Logic Array (PLA)
Definition:
A type of PLD with both programmable AND and OR gate arrays.
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Term: Programmable Array Logic (PAL)
Definition:
A PLD that has a programmable AND gate array and a fixed OR gate array.
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Term: Basic Functions
Definition:
Logic operations such as AND, OR, NOT commonly used in digital circuits.
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Term: Boolean Function
Definition:
A mathematical expression that uses Boolean algebra to define relationships between binary variables.