(Regular Logic Implementation Methods) An n-input majority function asserts its output whenever more than half of its inputs are asserted. You are to implement a seven-input majority function, which will assert its output whenever four or more of its inputs are asserted. Don't panic just because this is a seven-variable function. Build it up as a multilevel function whose subfunctions each have less than six variables. As a block diagram, it looks like Figure Ex. 4.26. Circuits #1 and #2 tally the number of their inputs that are asserted, providing the count in binary on the outputs (V, Y are the most significant bits; W, Z are the least significant bits). Based on these second-level inputs, Q determines if more than four or more of the original inputs are 1.

(a) Find the minimized sum-of-products form for Circuit #1 (Circuit #2 is identical). The functions V and W should look familiar. What do they implement?

(b) Complete a five-variable truth table for Circuit #3.

(c) Find the minimum sum-of-products form for Q using the K-map method.

(d) Find the minimum product-of-sums form for Q using the K-map method.

(e) How many 5-input look-up table CLBs would be required to implement this circuit? What if you only had 4-input CLBs?