Question

Please answer all 4 questions for a thumbs up! thank you

Create a Hierarchical Carry-Lookahead Adder which can handle 16-bit numbers and is split into four segments

1.How many bits will each segment handle?

2.What is the equation for c16 in terms of G3, P3, and c12?

3.In terms of G3, G2, G1, G0, P3, P2, P1, P0, and c0?

4.What is the equation for G2 in terms of g11, g10, g9, g8, p11, p10, and p9?

Answer 1

An adder of two 16-bit numbers contains 3 “floors”:

1. 16 ∑-components in the lower floor. The inputs to the i-th ∑-component are:x , :    i)xi,yi: the i-th pair of bits to be added ii)ci : the carry from the summation of xi-1,yi-1,ci-1 The outputs of the i-th ∑-component are: i)pi : an indicator whether the carry was propagated through the component. Computed using 1 level of logic: pi=xi xor yi ii)gi : an indicator whether the carry was generated in the component. Computed using 1 level of logic: gi=xiyi iii)si : the i-th bit of the result. si = pi ⊕ ci , therefore, once ci is available, it takes one more unit of time to compute si .
2. Four 4-bit carry lookahead generators in the second floor.
3. The third floor contains one carry lookahead generator. It is used to compute the input carries for the carry lookahead generators in the second floor, and to compute the “carry-propagated” and “carry generated” bits for the entire 16-bit adder.This bits can then be used either to compute the carry of the entire adder - c16

Answers to the questions:

1)Each segment handles 4 bits

2)c16=G3+P3c12

3)c16=G3+G2P3+G1P3P2+G0P3P2P1+P3P2P1C0

4)G2=g11+g10p11+g9p11p10+g8p11p10p9