Final answer:
To implement the function F(a,b,c,d) using a 4-16 decoder, we need to map the minterms to the outputs of the decoder based on their binary representations.
Step-by-step explanation:
To implement the given function F(a,b,c,d)=M3.M5.M9.M12 using a 4-16 decoder, we need to consider the minterms that are true (1) for the given function. Minterm M3 corresponds to the input combination a=0, b=1, c=1, d=1. Minterm M5 corresponds to a=1, b=0, c=1, d=0. Minterm M9 corresponds to a=0, b=1, c=0, d=0. Minterm M12 corresponds to a=1, b=1, c=1, d=0.
We can map these minterms to the 16 outputs of the 4-16 decoder. For example, M3 = 1000 in binary, so this would be connected to one of the outputs of the decoder that has its 4th input as 0 and the other inputs as 1. similarly, we can connect the other minterms to the appropriate outputs of the decoder based on their binary representations. Once all the minterms are connected, the outputs of the decoder will represent the function F(a,b,c,d).