please i want solve all this question with show all your work

1. Show how the function f(x, y, z) = m(1, 2, 4, 6, 7) can be implemented (a) using a 3-to-8 binary decoder and an OR gate (b) using a 3-to-8 binary decoder and an NAND gate (c) assume the function has one more input called z, implement the function using a 4-to-16 binary decoder and OR gate 2. Consider the function f = X7X3 + X7X2 + X2 X3.Derive a circuit for f that uses a ONE 2-to-1 multiplexer (a) using the truth table (b) using Shannon's expansion 3. Consider the function f = 77x3 + 27x2+xzxz. Derive a circuit for f that uses a 4-to-1 multiplexer (a) using the truth table (b) using Shannon's expansion 4. For the function f = x1x3 + x7x2 + X2 X3 . (a) find the cost of the circuit (b) use Shannon's expansion to derive a circuit that has a lower cost and give the cost of the circuit (Hint: apply Shannon's with respect to each input and find the cost)