Final answer:
To implement the function F(A,B,C) using a 4:1 multiplexer, assign A and B as select lines, with the inputs being D0='1', D1=C, D2='0', and D3=C, to match the defined minterms 0, 2, 5, and 6.
Step-by-step explanation:
To implement the Boolean expression F(A,B,C)=∑m(0,2,5,6) using a 4:1 multiplexer, we need to express the function in terms of the variables corresponding to the select lines of the multiplexer, typically the higher-order variables, here we'll take A and B. The multiplexer will select one of its four inputs depending on the combination of the select lines A and B.
For the given expression and a truth table for the min terms, we can deduce the inputs to the multiplexer. Here, minterms 0 and 2 correspond to when A and B are '00' and '01' respectively which means the value of C is irrelevant in these cases, so we need to pass a '0' when select lines are '00' and a '0' or '1' based on the value of C when select lines are '01'. Similarly, for minterms 5 and 6, which correspond to A and B being '10' and '11', the values at the multiplexer inputs should be decided by C.
Thus, the inputs to the multiplexer can be set as D0='1', D1=C, D2='0', and D3=C which corresponds to minterms 0, 2, 5, and 6.
The final setup will have A as the most significant bit (MSB) on the select line, B as the least significant bit (LSB), and the input to the multiplexer as the bit that corresponds to the value of C for the given minterms i.e., C for D1 and D3, while maintaining '1' and '0' for D0 and D2 respectively.