Understanding the Sklansky Adder Algorithm

[Narkon]

Hello. I am unsure if this subforum is the right place for this question, but without any alternatives, I will dare to post it here.

A few days ago I received an assignment which is about the creation in VHDL of a Sklansky adder. However, before I move to the coding part, I have trouble understanding the exact mechanics of the algorithm. Below you can see a pi is a picture I have found which shows the tree of a 16-bit Sklansky adder. I have already found the circuits that are represented by the black and grey boxes and I know that the triangles are just buffers.

Assuming we add the 16-bit A and B, I know that I have to find the generate and propagate values for each pair of bits A(i) and B(i) which are produced from the following equations

and

I also know that at some point I will have to calculate carry values with the equation:

but I can't find a detailed explanation about how all that ties together. I don't know which are the steps that take place after I get to the final "level" in the picture, which is depicted by the bottom most box (the one with the numbering 0:0, ... 15:0), and the professor who assign this has been less than helpful so far with cryptic explanations and confusing clarifications. I have no idea what happens after I am through with the black/grey components and the buffers. If someone can help me understand the basics and the flow of the algorithm, I will be grateful, even if it's only a link that offers the explanation I seek. Thank youhttp://i1140.photobucket.com/albums/n575/artdevil27/2015-12-12_183428_zpsvkvhsjvq.png?t=1449862983

 

[nilesh_pat]

The Sklansky adder is a type of ripple-carry adder. This means that each carry bit is generated by the previous carry bit and the two inputs being added. The way the Sklansky adder works is that it computes the generate (G) and propagate (P) values for each pair of bits, A(i) and B(i). The G and P values are used to compute the carry (C) values for each pair of bits, which are then used to compute the sum (S) values for each pair of bits. The G and P values are calculated using the following equations:G = A(i) & B(i)P = A(i) | B(i)The C values are then calculated using the following equation:C = C(i-1) + G + PFinally, the S values are calculated using the equation:S = A(i) ^ B(i) ^ C(i-1)To illustrate, let's take a look at the 16 bit Sklansky adder in the image you provided. Each triangle represents a buffer, which is basically a device that stores the value of the carry bit from the previous stage. The boxes with numbers represent the G, P, C, and S values for each bit. For example, the first box in the top row has the labels 0:G, 0:P, 1:C, and 0:S. This means that for the first bit (bit 0), the G and P values are calculated using the equation above, and the C value is taken from the buffer (which stores the carry bit from the previous stage). Finally, the S value is calculated using the equation above. The same process is repeated for each pair of bits, until the final sum is calculated.