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I have trouble understanding what's critical path delay of n-bit Ripple Carry Adder. In the book I read, given N-bit Ripple Carry Adder formed from N single 1-bit full adder:

  1. the critical path delay is 2N

    I know that for each single 1-bit full adder, the Cout(Carry-out)-delay is 2 and the Sum-delay
    is 3, from this observation why the critical path delay is not 2(N-1)+3 = 2N+1 (I mean the last one is calculated with Sum-delay instead of Cout-delay)? So assume that these 1-bit full adders are denoted by A(0) to A(N-1), the critical path delay is from Cin(A0) to Cout(A(N-1))? So I should not substitute the last one with Sum-delay?

  2. the delay to get the sum (Sum delay) is 2N+1

    I can understand this one, since now 2(N-1)+3 = 2N+1 should work, but isn't that this implicitly assumed that the last 1-bit full adder will be the slowest one? (You may skip this one if you want since my main focus is 1.)


Edit: I found a YouTube video explains why I mean, but I don't what whether he mean critical path delay.

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... why the critical path delay is not 2(N-1)+3 = 2N+1 (I mean the last one is calculated with Sum-delay instead of Cout-delay)?

Because although the initial data-to-Cout delay is 3 units, the final Cin-to-sum delay is in fact only 1 unit delay, which makes the final result simply 2N.

However, the Cout from the last stage has one more gate, resulting in 2N+1.

But the terminology seems backward to me. I would call the first one the "sum delay" and the second one the "critical path".

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I had originally posted an explanation that the delay from a least significant bit (lsb) input to the most significant bit (msb) output is 2n (provided that there are at least 2 full adders involved) because the critical path goes through the carry-out's of each full adder.

However, after thinking some more, I am convinced that you are correct, that the critical path delay is 2n+1. However, it is not from a lsb input to the msb output, but from a lsb input to the most-significant-less-1 output. There are 2n-2 delays from a lsb input to the input of a the final adder, and then 3 from that input to the sum output of that adder, which is the most-significant-less-1 output bit.

This assumes that full adders are implemented as a 3-bit majority gate and a 3-bit parity gate each composed of nand gates (which I believe gives the minimum delays - Cascading half adders, or xor gates implemented by nand gates, may appear simpler in diagrams, but actually add unnecessary delays).

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