Award Date

12-1-2013

Degree Type

Thesis

Degree Name

Master of Science in Electrical Engineering (MSEE)

Department

Electrical Engineering

First Committee Member

Yingtao Jiang

Second Committee Member

Emma Regentova

Third Committee Member

Mei Yang

Fourth Committee Member

Hui Zhao

Number of Pages

81

Abstract

High-performance, area-efficient hardware implementation of decimal multiplication is preferred to slow software simulations in a number of key scientific and financial application areas, where errors caused by converting decimal numbers into their approximate binary representations are not acceptable.

Multi-digit parallel decimal multipliers involve two major stages: (i) the partial product generation (PPG) stage, where decimal partial products are determined by selecting the right versions of the pre-computed multiples of the multiplicand, followed by (ii) the partial product accumulation (PPA) stage, where all the partial products are shifted and then added together to obtain the final multiplication product. In this thesis, we propose a parallel architecture for fixed-point decimal multiplications based on the 8421-5421 BCD representation. In essence, we apply a hybrid 8421-5421 recoding scheme to help simplify the computation logic of the PPG. In the following PPA stage, these generated partial products are accumulated using 8421 carry-lookahead adders (CLAs) organized as a tree structure; this organization is a significant departure from the traditional carry-save-adder-based (CSA) approach, which suffers from the problems introduced by extra recoding logic and/or addition circuits needed. In addition to the proposed 8421-5421-based decimal multiplier, we also propose a 4221-based decimal multi-plier that is built upon a novel full adder for 4221 BCD codes; in this design, expensive 4221-to-8421 conversions are no longer needed, and as a result, the operands of this 4221 multiplier can be directly represented in 4221 BCD.

The proposed 16x16 decimal multipliers are compared against other best known decimal multiplier designs in terms of delays and delay-area products with a TSMC 90nm technology. The evaluation results have confirmed that the proposed 8421-5421 multiplier achieves the lowest delay and is the most time-area efficient design among all the existing hardware-based BCD multipliers.

Keywords

BCD; Binary-coded decimal system; Coding; Coding theory; Computer architecture; Decimal fractions; Decimal multiplication; Multiplication

Disciplines

Computer and Systems Architecture | Computer Engineering | Electrical and Computer Engineering | Hardware Systems | Mathematics

Language

English