Designing a Combinational Circuit with Decision Points

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Objective:

The objective of this exercise is to enhance students' understanding of combinational circuit design by introducing decision points and more complex logic expressions.

Instructions:

$1.$ Problem Statement:

You are tasked with designing a combinational circuit that takes three inputs, A$,$ B$,$ and C$,$ and produces two outputs, X and Y$,$ based on the following logic expressions:

$-$ Output X should be true if either:

$-$ A is true and B is false, or

$-$ A is false and C is true.

$-$ Output Y should be true if both A and B are true, or if C is false.

$2.$ Requirements:

$-$ Incorporate at least two decision points in your circuit design.

$-$ Use a combination of logic gates $($AND$,$ OR$,$ NOT$)$ and decision$-$making logic to implement the circuit.

$-$ Clearly label the inputs $($A$,$ B$,$ C$)$ and outputs $($X$,$ Y$)$ on your circuit diagram.

$-$ Include a truth table showing all possible input combinations and their corresponding outputs $($X$,$ Y$).$

$-$ Ensure your circuit design accurately reflects the given logic expressions.

$3.$ Guidance:

$-$ Analyze the logic expressions provided and identify the decision points required to implement them.

$-$ Draw a schematic diagram of your circuit, indicating the decision points, logic gates, and connections between components.

$-$ Test your circuit by simulating different input combinations and verifying the outputs against the expected truth table.

$4.$ Submission:

$-$ Present your circuit diagram to the class, explaining your design approach and the rationale behind your decision points.

$-$ Demonstrate the functionality of your circuit by simulating input combinations and observing the outputs.

$-$ Submit your circuit diagram along with the corresponding truth table.

Additional Challenge $($Optional$)$:

$-$ Modify the circuit design to include an additional output Z$,$ which should be true if either:

$-$ A and B are both false, or

$-$ A and C are both true. Update your truth table accordingly.

$-$ Use the following to include specific decision points.

$1.$ Types of Decision Points:

$-$ Multiplexers $($MUX$)$: A multiplexer is a digital circuit that selects one of several input signals and forwards it to a single output line. The selection of the input signal is controlled by additional input lines known as select lines.

$-$ Demultiplexers $($DEMUX$)$: A demultiplexer is the opposite of a multiplexer. It takes a single input and routes it to one of several possible output lines based on the control input.

$-$ Decoder: A decoder is a combinational circuit that converts binary information from $\backslash ($n$\backslash )$ input lines to $\backslash (2^$n$\backslash )$ output lines, where each output line corresponds to a unique combination of input values.

$-$ Encoder: An encoder is the opposite of a decoder. It takes multiple input lines and generates a binary code corresponding to the active input line.

$2.$ Implementation of Decision Points:

$-$ Multiplexers and demultiplexers are commonly used to implement decision points in digital circuits. They provide a straightforward way to select and route signals based on control inputs.

$-$ Decoders and encoders can also be used to implement decision points by generating appropriate output signals based on the input values.

$3.$ Applications of Decision Points:

$-$ Data Routing: Decision points are used to route data between different parts of a circuit or between different devices.

$-$ Control Logic: Decision points play a crucial role in control logic circuits, where different actions need to be taken based on specific conditions or input values.

$-$ Addressing: In memory systems and communication protocols, decision points are used to select specific memory locations or communication channels based on address or control signals.

$-$ Arithmetic Logic Units $($ALU$)$: Decision points are essential components of ALUs, where arithmetic and logic operations are performed based on control signals and input values.

$4.$ Complexity and Design Considerations:

$-$ Implementing decision points increases the complexity of the circuit design and requires careful consideration of factors such as signal propagation delay, fan$-$out, and power consumption.

$-$ Designing efficient decision points involves optimizing the circuit for speed, area, and power while ensuring reliable operation under different conditions.

In summary, decision points are key components of digital circuits that enable branching behavior and conditional logic. They are implemented using multiplexers, demultiplexers, decoders, and encoders, and find applications in various areas such as data routing, control logic, addressing, and arithmetic logic units.