# Accession Number:

## AD0637761

# Title:

## DETERMINATION OF EXPECTED LONGEST CARRY PROPAGATION LENGTHS FOR BINARY ADDITION OF SIGNED NUMBERS.

# Descriptive Note:

## Technical rept.

# Corporate Author:

## NORTHWESTERN UNIV EVANSTON ILL INFORMATION-PROCESSING AND CONTROL SYSTEMS LAB

# Personal Author(s):

# Report Date:

## 1966-06-01

# Pagination or Media Count:

## 40.0

# Abstract:

The expected longest carry delay of asynchronous self-timing additions and the expected maximum number of processing cycles of synchronous iterative additions for signed binary numbers are exactly determined. The former depends on the longest carry propagation lengths due to either zero or nonzero carries, whereas the latter depends only on the longest nonzero carry propagation lengths. The signed numbers are represented by 2s complement notation. It is found that the enormous possible combinations for binary additions of signed numbers and their longest carry delays can be expressed by some recursive formulas if state representations of allowable addition processes without overflow are employed. By this method, efficient computer programmings are written to determine exactly the expected longest carry delays for asynchronous additions and the expected maximum numbers of processing cycles for synchronous iterative additions. The results for n 2 through n 48, where n is the number of bits of the summands, are given. The dependence relations of these delays on n are also considered. Author

# Descriptors:

# Subject Categories:

- Theoretical Mathematics
- Computer Programming and Software