This looks like homework. Our policy on homework is that you need to show your best effort to solve the problem so that we may help you with the areas that we can guide you to the solution. To that end I have some questions for you.

What single bit memory block would you use as a building block for an 8-bit register?​

What circuit would you use to decode three input bits to produce four outputs, where each output corresponds to one of the four functions?​

What circuit element is used to select one of n inputs to rout to an output?​

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This design approach is called divide an conquer.