Tom Kelliher, CS 315
Apr. 7, 1999
Adding N k-bit numbers using carry lookahead adders.
- Carry-Save addition.
Multiplication and convolution on linear arrays.
- Idea: Add three k-bit numbers in a single bit step, producing two
- Implementation: Use a binary full adder for each bit position,
producing a low order bit and a carry bit for each bit position.
- The final sum is the sum of the low order bits and the shifted carry
- Time required to reduce the sum of N k-bit numbers to the sum of
two -bit numbers: bit steps.
- After the first step of CSA, how many numbers are we left with?
(At most . Why?)
- After the second step?
- After the jth step:
- After steps, we're left with numbers, so we need steps to reduce to two -bit numbers.
- Use a carry lookahead adder to reduce the two-number
redundant representation to a single, non-redundant number.
- Example: Draw the Wallace tree for N = 9.
How is multiplication like adding N k-bit numbers?
How can we use what we just learned to multiply? Must we add anything?
Thomas P. Kelliher
Wed Apr 7 10:56:50 EDT 1999