Final answer:
The student's question involves implementing a Boolean function using a 4-to-16 active low decoder and external AND gates, incorporating both minterms and don't care conditions.
Step-by-step explanation:
The student is asking how to implement a Boolean function with a given minterm and don't care conditions using a 4-to-16 active low decoder and external AND gates.
In digital electronics, minterm represents a specific combination of variables where the function output is 1, and don't care conditions are the cases where the output can be either 0 or 1 without affecting the functionality -- these conditions can be used to simplify the circuit.
A 4-to-16 decoder outputs a low signal (0) for the selected output corresponding to the binary input value when enabled, with all non-selected outputs being high (1).
To use the 4-to-16 decoder for implementing function F, it is required to connect the AND gates to the appropriate output lines of the decoder that correspond to the minterm indices (0, 3, 4, 7, 12, 14) and don't care indices (1, 6, 9, 10, 11, 13) since these are active-low outputs.
The AND gate inputs will be the decoder outputs that are active-low when the input ABCD is equal to the minterm or don't care index. By doing so, any one of the AND gates will output a low (0) when its conditions are met, which means the function output will be high (1) due to the active-low nature of the decoder output.