If we rotate some of your indicies, it forms the correct carry out. Cout will be P3P2P1P0Cin + P3P2P1G0 + P3P2G1 + P3G2 + G3
The double indices aren't extremely important, but in the blue box just above that, it defines P[i:i] to be Ai xor Bi and G[i:i] to be Ai * Bi.
With i representing the index of the first number and j being the index of the second number. Because they have the same weight, 2^(i), they already work together just fine. k represented the weight of the values being considered. So G[k-1:j] comes from the product (AND) of two numbers of weight 2^(k-1) while P[i:k] comes from the parity (XOR) of two numbers of weight 2^k. The other thing is that those wires in the box drawings all represent two trace wires one for P and one for G.
I'm surprised you didn't ask what the cube meant. Two of its dimensions are actually of some significance in minecraft.
The double indices aren't extremely important, but in the blue box just above that, it defines P[i:i] to be Ai xor Bi and G[i:i] to be Ai * Bi.
With i representing the index of the first number and j being the index of the second number. Because they have the same weight, 2^(i), they already work together just fine. k represented the weight of the values being considered. So G[k-1:j] comes from the product (AND) of two numbers of weight 2^(k-1) while P[i:k] comes from the parity (XOR) of two numbers of weight 2^k. The other thing is that those wires in the box drawings all represent two trace wires one for P and one for G.
I'm surprised you didn't ask what the cube meant. Two of its dimensions are actually of some significance in minecraft.