The prefix network shown in Figure 5.7 uses black cells to compute all of the prefixes. Some of the block propagate signals are not actually necessary. Design a “gray cell” that receives G and P signals for bits i:k and k−1:j but produces only G_i:j, not P_i:j. Redraw the prefix network, replacing black cells with gray cells wherever possible.

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14 13 12 11 10 9 8 1 0 15 7 5 3 2 -1 14:13 12:11 10:9 8:7 6:5 4:3 2:1 0:-1 14:11 13:11 10:7 9:7 6:3 5:3 2:-1 1:-1 14:7 13:7 12:7 11:7 6:-1 5:-1 4:-1 3:-1 14:-1 13:-1 12:-1 11:-1 10:-1 9:-1 8:-1 |7:-1 15 14 13 12 11 10 9 7 6 Figure 5.7 16-bit prefix adder Legend i:j A; B; G-1-1A; B; Pii G Pii S; 4,