In the design of parallel prefix adders (PPA), the P/G-combining logic node can combine the P's and G's from two adjacent "groups" of bits together as shown in the class. Answer the following questions (a) Represent G6:4 and P64 in terms of the necessary bit-wise g's and p's (b) When combining two bit-groups: (11 9) and (8:7) to find the P/G for the group (11: 7), answer the following questions: i. Give the logical expression of G11:7 and P1:7 in terms G119, P119 and Gs:7, Ps:7- ii. Represent the outgoing carry of this group c12 in terms of Gi1, P11:7 and the incoming carry cr iii. If the two input numbers to be added have the following bit pattern within this group as: a01010 and b1:7110, determine the value of the each of the following: (G9, P11:9), Gs:7, P:7), and (G11, P1:7) (c) Pertaining to the 32-bit Kogge-Stone PPA, answer each of the following questions i. How many levels of P/G combining logic are required? ii. Show how c is obtained? That is, how are G26:0 and P260 derived? Show the the combination steps in details using a tree structure as depicted in the class, and show the group range (e.g. (15:1 at the output of each P/G-combining logic node iii. How long does it take for 827 to be finalized in the worst case in terms of d? (d) Repeat (c) for the 32-bit Brent-Kung PPA In the design of parallel prefix adders (PPA), the P/G-combining logic node can combine the P's and G's from two adjacent "groups" of bits together as shown in the class. Answer the following questions (a) Represent G6:4 and P64 in terms of the necessary bit-wise g's and p's (b) When combining two bit-groups: (11 9) and (8:7) to find the P/G for the group (11: 7), answer the following questions: i. Give the logical expression of G11:7 and P1:7 in terms G119, P119 and Gs:7, Ps:7- ii. Represent the outgoing carry of this group c12 in terms of Gi1, P11:7 and the incoming carry cr iii. If the two input numbers to be added have the following bit pattern within this group as: a01010 and b1:7110, determine the value of the each of the following: (G9, P11:9), Gs:7, P:7), and (G11, P1:7) (c) Pertaining to the 32-bit Kogge-Stone PPA, answer each of the following questions i. How many levels of P/G combining logic are required? ii. Show how c is obtained? That is, how are G26:0 and P260 derived? Show the the combination steps in details using a tree structure as depicted in the class, and show the group range (e.g. (15:1 at the output of each P/G-combining logic node iii. How long does it take for 827 to be finalized in the worst case in terms of d? (d) Repeat (c) for the 32-bit Brent-Kung PPA