Question

Implement each of the following functions using a multiplexer.

(x, y, z) = ∑(0,2,5,7)

Answer 1

To implement the given sum of minterms function using a multiplexer, translate the function into a truth table, use a 4-to-1 MUX, set the appropriate inputs to high for the specified minterms, and configure the selection lines using the x, y, z variables.

Step-by-step explanation:

Implementing a Function Using a Multiplexer

To implement the function f(x, y, z) = ∑(0,2,5,7), which indicates a Sum of Minterms, using a multiplexer (MUX), one must first translate this into a truth table and then determine the appropriate inputs for the MUX. In digital logic, a multiplexer acts as a switch that selects one of several input signals and forwards the selected input into a single line. A multiplexer is identified by its number of inputs and the number of selection lines required to select between those inputs.

A 4-to-1 multiplexer will be adequate here since we need to select between four minterms. Each selection line represents a binary decision based on the inputs (x, y, z). For the given function, you can map the binary representations of 0, 2, 5, and 7 to the multiplexer inputs, ensuring that when the selection lines pick any combination representing these numbers, the output is '1'.

The selection lines will be holding the variables, and the data inputs will be high (1) for the minterms corresponding to the function. For all other minterms (1, 3, 4, and 6), the input should be low (0). To configure the multiplexer properly, assign the variables as follows: Selection lines 's1' and 's0' can be associated with 'y' and 'z', and use 'x' to determine which input lines on the MUX should be high.

Steps to Implement the Function

1. Determine the minterm values for the function (0, 2, 5, 7) and convert them to binary.
2. Map these values to the multiplexer inputs, setting them to high.
3. Configure the selection lines based on the y and z variables.
4. Use the x variable to decide which inputs to assert (in this case, inputs equivalent to the minterms).
5. Verify the MUX outputs the correct value for each combination of x, y, and z by cross-referencing with the truth table.

In conclusion, the MUX will output the correct value for the specified minterms when the correct inputs and selection lines are configured.