Final answer:
The student's question involves designing circuitry to implement a Boolean function using a 4-to-16 active-low decoder and external AND gates, based on specified minterms and 'don't care' conditions.
Step-by-step explanation:
The student is asking how to implement a Boolean function using a 4-to-16 active-low decoder and external AND gates. To do this, we need to utilize the minterms given by the function F(A,B,C,D) = Σm(0,3,4,7,12,14) along with the indeterminate entries d(A,B,C,D) =Σd(1, 6, 9, 10, 11, 13).
With the active-low decoder, each output corresponds to a minterm, i.e., when one specific combination of inputs is provided, the corresponding output goes low. The outputs representing the minterms of F will be connected to AND gates as needed to implement the function with active-high logic.
For instance, to obtain minterm 0 (A=0, B=0, C=0, D=0), we would take the output 0 from the decoder, which would be active-low for this combination, and connect it to an AND gate. The same is done for each required minterm. If OR functions are needed, they can be simulated using multiple AND gates by taking advantage of De Morgan's theorem.
Indeterminate entries, represented by 'don't care' conditions, give flexibility in simplifying the overall circuit as they can be treated as either 1 or 0 in terms of function optimization.