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Manu · Accepted Answer

Step 1: To implement a XOR gate using Tri-State Buffers and following the hint of initially solving with a 4-to-1 multiplexer, let's break down the process: XOR Function The XOR (exclusive OR) function outputs true only when the inputs differ. In binary terms: XOR(0, 0) = 0 XOR(0, 1) = 1 XOR(1, 0) = 1 XOR(1, 1) = 0 Using a 4-to-1 MUX A 4-to-1 multiplexer selects one of four input lines based on two control lines (A and B here). Here’s how to map the XOR function onto a 4-to-1 MUX: Input Line 0: This corresponds to both control lines being 0 (A=0, B=0). Output should be 0. Input Line 1: This corresponds to control line A=0, B=1. Output should be 1. Input Line 2: This corresponds to control line A=1, B=0. Output should be 1. Input Line 3: This corresponds to control line A=1, B=1. Output should be 0. MUX Connection Connect the inputs of the MUX to fixed values based on the desired XOR output for each control line combination: Input 0 = 0 Input 1 = 1 Input 2 = 1 Input 3 = 0 Implementing with Tri-State Buffers Tri-State buffers can be used to control which output is actively driving the line: Connect two buffers to each input (0 or 1): One buffer for each value of A (either 0 or 1). Control Lines: Use A and B to control which buffer is active. This can be done by connecting: Buffer enable for input 0 with NOT A AND NOT B. Buffer enable for input 1 with NOT A AND B. Buffer enable for input 2 with A AND NOT B. Buffer enable for input 3 with A AND B. Logical Connections The output of the XOR gate is the output from the active buffer, which will depend on the state of A and B. Explanation: To implement a XOR gate using tri-state buffers and a 4-to-1 MUX, connect the outputs of fixed logical values (0 or 1) to the MUX inputs, controlled by the states of A and B, then selectively enable the correct buffer using the combination of A and B to produce the XOR output. Step 2: Truth table for the XOR gate using the 4-to-1 MUX, showing the control inputs, their corresponding MUX inputs, and the resulting XOR output: Explanation: This table maps the control inputs (A and B) to their respective MUX inputs based on the desired XOR operation and shows the output of the XOR operation for each combination of inputs. This diagram a XOR gate implementation using a 4-to-1 multiplexer, where the control inputs A and B select between fixed logical values (0 or 1) corresponding to the XOR truth table to produce the XOR output. Final Answer: The diagram effectively demonstrates the implementation of a XOR gate using a 4-to-1 multiplexer and tri-state buffers. By leveraging the control inputs A and B to select appropriate MUX inputs corresponding to the XOR truth table, we can achieve the desired XOR functionality. This method highlights the versatility of multiplexers in digital circuit design, providing a clear and efficient way to realize complex logic functions.

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