Question

Question: First, show the block organization of the 16-bit carry save adders to add these 16 terms, as shown in Figure B.14.1. Assume that the time delay through each 1-bit adder is 2T. calculate the time of adding four 4-bit numbers to the organization at the top versus the organization at the bottom of Figure B.14.1.

Short answer

Answer

The block organization of the 16-bit carry save adder:

The delay in a ripple carry adder is 32T and in carry save adder is 12T

Step-by-step solution

Block organization of 16-bit carry save adder

The carry bit save adder for 16-bit has 16 adders. It consists of a parallel 16 adders without any horizontal connection. It adds two 16-bit integers and produces two values sum and carry. The block organization of the 16-bit carry save adder:

Calculation of delay in a ripple carry adder

The delay in the ripple carry adder is calculated using the following formula:

Here, m is the number of operands and n is the number of bits.

For the rippler carry adder given in the question, the delay is:

 Step 3: Calculation of delay in carry save adder

Since the inputs in the carry save adder are applied in parallel, the delay is equal to the delay of an adder. To add four numbers, the delay for the carry save adder is: