# A study of arithmetic circuits and the effect of utilising Reed-Muller techniques.

Guan, Zhigang (1995) A study of arithmetic circuits and the effect of utilising Reed-Muller techniques. PhD thesis, Edinburgh Napier University.

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## Abstract/Description

Reed-Muller algebraic techniques, as an alternative means in logic design, became
more attractive recently, because of their compact representations of logic functions
and yielding of easily testable circuits. It is claimed by some researchers that ReedMuller
algebraic techniques are particularly suitable for arithmetic circuits. In fact, no
practical application in this field can be found in the open literature.
This project investigates existing Reed-Muller algebraic techniques and explores their
application in arithmetic circuits. The work described in this thesis is concerned with
practical applications in arithmetic circuits, especially for minimizing logic circuits at
the transistor level. These results are compared with those obtained using the
conventional Boolean algebraic techniques. This work is also related to wider fields,
technology in VLSI. The emphasis is put on circuit level (transistor level) design. The
results show that, although Boolean logic is believed to be a more general tool in logic
design, it is not the best tool in all situations. Reed-Muller logic can generate good
results which can't be easily obtained by using Boolean logic.
F or testing purposes, a gate fault model is often used in the conventional implementation of Reed-Muller logic, which leads to Reed-Muller logic being
restricted to using a small gate set. This usually leads to generating more complex
circuits. When a cell fault model, which is more suitable for regular and iterative
circuits, such as arithmetic circuits, is used instead of the gate fault model in ReedMuller
logic, a wider gate set can be employed to realize Reed-Muller functions. As a
result, many circuits designed using Reed-Muller logic can be comparable to that
designed using Boolean logic. This conclusion is demonstrated by testing many
randomly generated functions.
The main aim of this project is to develop arithmetic circuits for practical application.
A number of practical arithmetic circuits are reported. The first one is a carry chain
adder. Utilising the CMOS circuit characteristics, a simple and high speed carry chain
is constructed to perform the carry operation. The proposed carry chain adder can be
reconstructed to form a fast carry skip adder, and it is also found to be a good
application for residue number adders. An algorithm for an on-line adder and its
implementation are also developed. Another circuit is a parallel multiplier based on
5:3 counter. The simulations show that the proposed circuits are better than many
previous designs, in terms of the number of transistors and speed. In addition, a 4:2
compressor for a carry free adder is investigated. It is shown that the two main
schemes to construct the 4:2 compressor have a unified structure. A variant of the
Baugh and Wooley algorithm is also studied and generalized in this work.

Item Type: Thesis (PhD) Reed-Muller; logic design; arithmetic circuits; logic circuits; CMOS; carry chain; Faculty of Engineering, Computing and Creative Industries > School of Engineering and the Built Environment 600 Technology > 620 Engineering > 621 Electronic & mechanical engineering > 621.3 Electrical & electronic engineering T Technology > TK Electrical engineering. Electronics Nuclear engineering 4340 Mrs Lyn Gibson 15 Apr 2011 13:43 15 Apr 2011 13:43 http://researchrepository.napier.ac.uk/id/eprint/4340