Final answer:
To realize the given functions using a 4-to-16 decoder module and output logic gates, we need to map the inputs to the corresponding decoder output lines and implement the logic using NAND or AND gates. Then, we can minimize the functions using Boolean algebra or a Karnaugh map.
Step-by-step explanation:
To realize each of the given functions using a 4-to-16 decoder module and output logic gates, we need to map the inputs to the corresponding output lines of the decoder. Then, we can use NAND or AND gates to implement the logic of the function for each output line.
For the function fi(a,b,c,d) = m(2,4,10,11,12,13), the inputs (a,b,c,d) are mapped to the following decoder output lines: (0110, 1001, 1010, 1011, 1100, 1101). Using NAND or AND gates, we can implement the logic for each output line.
Similarly, for the function f(a,b,c,d) = m(3,6,9,12,14,15), the inputs (a,b,c,d) are mapped to the following decoder output lines: (1100, 0100, 0010, 0001, 1111, 1110). Lastly, for the function fz(a,b,c,d) = 5c + abd, we need to express it in terms of minterms and minimize it to a sum of products using Karnaugh map or Boolean algebra.