**Tom Kelliher, CS 315**

**Mar. 3, 1999**

Read 1.2.3.

Carry lookahead addition.

- Introduction.
- Computing the prefixes.

Carry save addition.

- General form of a prefix computation:
where is a function of an input bit.

- Consider carry lookahead addition. Let be the s, p, or g for
bit position
**i**. Then:Note that this is written ``backwards.''

Why the initial s?

- Multiplication table for carry lookahead addition:
This operation must be associative for the carry computation to work. Why? Show.

What's going on here?

- Using a four-leaf tree, label each leaf with it's and
values.
- Can the class derive the calculation for the tree? Hint: each vertex
in the tree stores the product of its sub-tree leaves.
- General idea:
- Rising phase: each vertex computes the product of inputs from its
children. Action of a leaf, internal vertex.
- Computed values are passed from left child to right child.
- Falling phase: each internal vertex takes received value and
transmits it to children. Leaves concatenate received values on left.

- Rising phase: each vertex computes the product of inputs from its
children. Action of a leaf, internal vertex.
- Show an example on a nine-leaf tree.

Wed Mar 3 11:16:47 EST 1999