Final answer:
To implement f(w,x,y,z) using two 8-way multiplexers and an OR gate, you distribute minterms among the multiplexer inputs, configure the enables accordingly, and combine their outputs using the OR gate.
Step-by-step explanation:
To implement the function f(w,x,y,z)=∑m(0,1,5,7,8,10,13,14,15) using two 8-way multiplexers (MUX) with an active low enable, plus an OR gate, we start by expressing the function in terms of the possible inputs of the multiplexers. Generally, an 8-way multiplexer selects one of 8 inputs based on a 3-bit selection input. In this case, we can use three of the function's variables (w, x, and y) as selection inputs and the fourth variable (z) as part of the data inputs. The minterms can be distributed among the two multiplexers, configuring their data inputs to represent the function's output for each minterm.
For instance, the first multiplexer can handle minterms 0, 1, 5, and 7 by setting its corresponding data inputs D0-D7. D0 will be set to 1 for minterm 0, D1 will be set to 1 for minterm 1, D5 will be set to 1 for minterm 5, and D7 will be set to 1 for minterm 7. All other data inputs for this multiplexer should be set to 0 since they do not represent required minterms.
The second multiplexer will handle minterms 8, 10, 13, 14, and 15 with a similar approach. The OR gate comes into play to combine the outputs of both multiplexers such that when either one outputs a 1, indicating the presence of a corresponding minterm, the final function output is 1.
Here's an illustrative configuration: Multiplexer A handles wxy=(000, 001, 101, 111) with an enable tied to z' (NOT z), and Multiplexer B handles wxy=(1000, 1010, 1101, 1110, 1111) with an enable tied to z. The OR gate would be used to combine the outputs of Multiplexer A and B.
The configuration ensures that only when the enable is active (LOW for an active low enable), will the multiplexer's output affect the final function, thereby, correctly implementing the function using an OR gate to synthesize the final output.