hat is a Multiplexer? Design a Four-To-One-Line Multiplexer

A **Multiplexer** (often abbreviated as MUX) is a combinational circuit that selects one of several input signals and forwards the selected input to a single output line. The selection of the input is controlled by a set of selection lines. Multiplexers are widely used in digital circuits for data routing, signal switching, and resource sharing. ### Four-To-One-Line Multiplexer A **Four-To-One-Line Multiplexer** has four input lines, two selection lines, and one output line. The selection lines determine which of the four inputs is connected to the output. #### Inputs and Outputs - **Inputs**: \( I_0, I_1, I_2, I_3 \) (4 inputs) - **Selection Lines**: \( S_0, S_1 \) (2 selection lines) - **Output**: \( Y \) (1 output) #### Truth Table The truth table for a 4-to-1 multiplexer is as follows: | \( S_1 \) | \( S_0 \) | Output \( Y \) | |-----------|-----------|-----------------| | 0 | 0 | \( I_0 \) | | 0 | 1 | \( I_1 \) | | 1 | 0 | \( I_2 \) | | 1 | 1 | \( I_3 \) | #### Logic Diagram The logic diagram for a 4-to-1 multiplexer can be constructed using AND, OR, and NOT gates. Here’s how it works: 1. **Selection Lines**: The selection lines \( S_0 \) and \( S_1 \) determine which input is selected. 2. **AND Gates**: Each input is connected to an AND gate, which is enabled based on the selection lines. 3. **OR Gate**: The outputs of the AND gates are fed into a single OR gate, which produces the final output. #### Logic Expression The output \( Y \) can be expressed as: \[ Y = (I_0 \cdot \overline{S_1} \cdot \overline{S_0}) + (I_1 \cdot \overline{S_1} \cdot S_0) + (I_2 \cdot S_1 \cdot \overline{S_0}) + (I_3 \cdot S_1 \cdot S_0) \] Where: - \( \overline{S_1} \) and \( \overline{S_0} \) are the NOT operations on the selection lines. ### Implementation 1. **AND Gates**: - \( AND_0 \) for \( I_0 \): Input \( I_0 \) and \( \overline{S_1} \) and \( \overline{S_0} \) - \( AND_1 \) for \( I_1 \): Input \( I_1 \) and \( \overline{S_1} \) and \( S_0 \) - \( AND_2 \) for \( I_2 \): Input \( I_2 \) and \( S_1 \) and \( \overline{S_0} \) - \( AND_3 \) for \( I_3 \): Input \( I_3 \) and \( S_1 \) and \( S_0 \) 2. **OR Gate**: - The outputs of the four AND gates are connected to a single OR gate to produce the final output \( Y \). ### Conclusion A 4-to-1 multiplexer is a fundamental building block in digital electronics, allowing for the selection of one of several inputs based on binary selection lines. It can be implemented using basic logic gates, making it a versatile component in various applications, including data routing and signal processing.