You need to compare the delay and cost analysis of 3 different adders listed bel

Question

You need to compare the delay and cost analysis of 3 different adders listed below. These adders will be wired in a way that you are trying to calculate the sum of adding 2 16-bit numbers. It is suggested that you calculate cost of a single unit and then multiple that single unit by the number of modules needed to make the full 16-bit circuit. 1. Calculate the Maximum delay times that will occur for the complete Sum and the Carryout bit of a Ripple Carry Adder consisting only of 16 Full Adder (2-level) modules 2. Calculate the Maximum delay times that will occur for the complete Sum and the Carryout bit of a Carry Look-ahead Adder without a gate fan in limitation 3. Calculate the Maximum delay times that will occur for the complete Sum and the Carryout bit of a carry Look-ahead Adder that consists of 4 connected 4-bit Carry look-ahead adder blocks. (See pages 148-151 of the textbook to help).

Explanation / Answer

1. The maximum delay that occurs in a 16 bit ripple adder is 16T units. The ripple adder adds 16 bits parallels but the carry must ripple their way from the least significant bit to the most significant bit and it takes T units for the carry to reach the input of the next bit and since there are 16 bits the total delay will be 16T units.

2. For carry look ahead adder the carry bit is calculated once the input is given and thus reduces the delay. It requires the calculation of propagate and generate signals. One delay is caused by the propagate signal two delay is caused by the AND and OR operations due to generate signal, then one more delay is caused by the sum bit thereby the total delay will be 4T units.

3. For a 4-bit carry look ahead adder the propagation delay will be 4T units just as explained above in 2, its delay doesn't depend on the number of bits added or the number of blocks required

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