Implement a 32-to-1 multiplexer using two 16-to-1 multiplexers and a 2-to-1 multiplexer in two ways: (a) Connect the most significant select line to the 2-to-1 multiplexer, and (b) connect the least significant select line to the 2-to-1 multiplexer.
The correct answer and explanation is :
A 32-to-1 multiplexer (MUX) selects one of 32 input signals and forwards it to a single output line, controlled by five select lines (S₄, S₃, S₂, S₁, S₀). We can construct such a MUX using two 16-to-1 MUXs and one 2-to-1 MUX. This can be achieved in two configurations:
(a) Connecting the Most Significant Select Line (S₄) to the 2-to-1 MUX:
In this configuration, the most significant select line, S₄, determines which of the two 16-to-1 MUXs is active. The remaining select lines (S₃, S₂, S₁, S₀) are connected in parallel to both 16-to-1 MUXs. Each 16-to-1 MUX handles 16 of the 32 input signals:
- First 16-to-1 MUX: Connects to inputs I₀ through I₁₅.
- Second 16-to-1 MUX: Connects to inputs I₁₆ through I₃₁.
The outputs of these two 16-to-1 MUXs are then fed into the 2-to-1 MUX. The select line S₄ controls the 2-to-1 MUX:
- S₄ = 0: Selects the output from the first 16-to-1 MUX.
- S₄ = 1: Selects the output from the second 16-to-1 MUX.
This setup ensures that the correct input (I₀ to I₃₁) is routed to the output based on the combination of the select lines.
(b) Connecting the Least Significant Select Line (S₀) to the 2-to-1 MUX:
Alternatively, the least significant select line, S₀, can control the 2-to-1 MUX. In this arrangement:
- First 16-to-1 MUX: Connects to inputs I₀, I₂, I₄, …, I₃₀ (even-numbered inputs).
- Second 16-to-1 MUX: Connects to inputs I₁, I₃, I₅, …, I₃₁ (odd-numbered inputs).
The remaining select lines (S₄, S₃, S₂, S₁) are connected in parallel to both 16-to-1 MUXs. The outputs of these MUXs are then fed into the 2-to-1 MUX, with S₀ determining the final output:
- S₀ = 0: Selects the output from the first 16-to-1 MUX (even inputs).
- S₀ = 1: Selects the output from the second 16-to-1 MUX (odd inputs).
This configuration also ensures that the correct input is routed to the output based on the select lines.
Explanation:
In both configurations, the 32 inputs are divided between the two 16-to-1 MUXs. The 2-to-1 MUX then selects which 16-to-1 MUX’s output to forward based on one of the select lines. The choice of which select line to connect to the 2-to-1 MUX (most significant or least significant) affects how the inputs are assigned to the 16-to-1 MUXs but achieves the same overall functionality.
Visual Representation:
For a detailed visual representation of these configurations, you can refer to the following resource:
- Implementing a 32-to-1 Multiplexer Using Two 16-to-1 Multiplexers and a 2-to-1 Multiplexer:
This resource provides diagrams and further explanations on how to implement a 32-to-1 MUX using the described methods.
Understanding these configurations is crucial for designing efficient digital systems, as multiplexers play a vital role in routing signals within integrated circuits.