Mumbai University > Computer Engineering > Sem 8 > parallel and distributed systems

Marks: 10M

Arithmetic pipelines like floating point multiplications are popular in general purpose computers and question actually arises, when a pipe lining can be used. We have seen that, pipe lining can be used whenever you are getting continuous input and producing continuous output.

For a single task, it does not give you any benefit, the reason for that is, for a single task, time required to perform computation execution is more than that of a non pipeline implementation.

That means, only when large number of tasks are to be performed then pipeline is suitable.

whenever you are performing multiplication of two numbers, say A and B, say is equal to let us assume 1011 and the number another number is 1010. So, whenever you have to multiplier, what you do, whenever you do by hand computation, you first multiply 0 with this, so you get 1011 then multiply 1 with, you multiply with 0, you will get 0000. Whenever you multiply with 1, you get 1011 and you

keep on shifting it and you essentially, we do shift and add, shift and you have to add these two numbers.

You have perform addition of this and then whenever you multiply with this, again you get 0000 and then another is 1011. So now, these are added, so this addition whenever you perform by hand, we may do it simultaneously that means, we add all these bits together and produce the sum, as it is shown in this diagram below here, A and B, two 8 bit numbers, P 0 is a partial product. By multiplying this bit one with this number, all the bits, we get this and in this way, we have got partial product P 0, P 1, P 2, P 3, P 4, P 5, P 6 and P 7 corresponding to multiplication of these 8 bits with these bits.

So, these are the partial products, which are to be added and you can see 0 has been inserted on the right side. And whenever we do the addition of the entire column, but whenever you do it with the help of practical I mean processors, your adder will take two numbers, usual symbol of adder is this, adder will take two numbers and produces sum and a carry. So, this A, B, sum and carry, so you cannot really perform all these additions simultaneously, which is shown in this diagram.

However, we can try to do it in a pipelined manner , instead of doing it serially that means, adding these two P 0 and P 1 then P 0 and P 1 then the result of that is added with P 2. And then result of that is added with P 3 and so on, that is essentially doing it serially, that will take long time. It will take definitely 8 clock cycles, if we perform one addition per clock cycle.

Diagram