Optimization of Delay IIN Pipeline Mac Unit Using Wallace Tree Multiplier

Abstract

A prompt pipelined MAC unit is implemented in this paper. Due to carrying propagations in additions, including additions of multiplications and additions of accumulations, we will experience a significant path delay as well as a significant increase in power consumption when using the conventional methodology. To resolve these issues, we are including a portion of improvements to the partial product reduction procedure. The pipelined MAC implementation does not complete the addition and accumulation of the most weighted bits until the partial product reduction step of the subsequent multiplication. In order to manage the overspill bits during the partial product reduction procedure, we are designing the small size adder which computes the total number of carries. By comparing with the conventional methodologies, we will get the diminished area as well as power consumption for the proposed pipelined MAC implementation.

Introduction

I. INTRODUCTION

In digital signal processing applications, the Multiply Accumulate unit is the primitive block. Digital Signal processors (DSP) are used widely in applications like speech and audio coding, image processing, video processing, etc., most of these applications require sequential algorithms, and the DSPs chip Architecture is designed to perform sequential tasks. Computation of these applications involves multiplication as well accumulation operations & hence Multiply Accumulate (MAC) unit is very imperative in DSP applications, to achieve these applications in real-time with high performance. In the past, several methodologies were performed in scheming MAC structural designs through great computational effectiveness as well as enhanced power consumption.

A traditional mac is mainly composed of two main blocks namely multiplier and accumulator An A n-bit mac unit will have n bit multiplier and (2n+∝-1)  adders. The alpha bits are the overload bits. Multipliers’s role in today’s digital signal processing and various other applications is crucial. Addition and multiplication are the most widely used basic operations in high-end applications. If observed keenly, almost 70-75% of instructions in microprocessor and other DSP require addition and multiplication. In mac also, adder and multiplier are the basic blocks. The designer mainly concentrates on the design of a circuit that is both fast and energy-efficient.

The Wallace tree, array, and other multipliers are just a few examples of multipliers, the  Wallace tree multiplier showed better performance and for addition among various adders such as ripple carry adder, carry skip adder, carry save adder, and carry select adder, parallel prefix adders are considered as best choice.

A novel MAC design for high-speed achievement is proposed. Our first idea is to incorporate the integration of adders, which includes a portion that is a component of the accumulation's final addition as well as of the multiplication's final addition. In order to cut down on power use and critical path time, there is also the partial product reduction method. The most crucial bits are not finally included during the current multiplication in the suggested MAC unit. The second stage of partial product reduction involves the final addition and aggregation of the most significant bits.

Pipelining is the process of accumulating instruction from processor to through a pipeline. Instructions enter from one end as well as leaves from another end. The use of a pipeline improves the design's overall throughput. The pipeline itself interpreted into different stages, which would then be linked together as well as to create a pipeline configuration.

The MAC unit's entries were retrieved through memory cells as well as transmitted to a multiplication block, it conducts multiplication as well as transfers the outcome to the adder, who then preserves the outcome in a memory region. This entire procedure should be done in one clock cycle. For this configuration, the accumulator is a carry selection adder.

A. Multiplier Unit

Multipliers are used in multiply accumulate unit, generally in multiplier have three parts those are partial product generation and accumulation and final product we will get after reduced to two rows. Partial products are generated by using and gates and accumulation of partial products are done by using full adder as well as half adders. Here carry propagations are not allowed. If the carry propagations are performed here the propagation delay of overall circuit is increased drastically.

B. Adder Unit

Not only the multiplier but also adders greatly influence MAC performance. Hence design-performance full adder is needed for the day. Different adders circuit are analysed in order to choose the appropriate adder for improving the performance of MAC Unit. Initially ripple carry adder is studied. Due to the  high delay it is not preferred. Later carry skip adder is analyzed. Although the speed is improved compared to ripple carry adder, it is not effectively reduced. next   carry save adder is analyzed .although parallel operation is performed in the initial stages it uses carry propagation in its final stage which is not preferred. finally parallel prefix adders, from the analysis can be observed as the best choice for applications like MAC and DSP.

II. RELATED WORKS

The two stage MAC unit structure was shown in Fig. 2. It is composed of three stages termed as formation of partial products, accumulation of partial products, as well as alpha-bit addition.

The central MAC device is made up of

1. Generation of  PP
2. Reduction of  PP
3. Alpha-bit addition

For forming the partial products in the unsigned MAC structure and gates can be directly utilized. Various partial product generation algorithms are known to produce signed Partial product matrix for signed MAC unit. To construct the signed partial product matrix, we used the Baugh-Wooley multiplier algorithm.

The multiplication procedure for unsigned MAC unit:

The first stage in the MAC unit design is partial product generation and the PPM can be obtained by placing the register accumulation bits with the stage of partial product development.

The accumulation process has progressed to the second level, here we will perform the (k+α ) bit addition. In this accumulation stage we will utilize carry propagate adder in the last row of the LSB position only. Based on Dadda multiplication approach we will reduce the partial product array to two rows without utilizing carry propagations. The proposed block diagram for this work is shown below.

Overflow bits can be handled by α  –bit adder. Based on number of bits considering to perform Pipelined MAC unit the α  –bit adder width will alter. Depending on bit width we need to change the addition of α  –bit adder design. For accumulating the partial products, full adders and half adders are used and the carries generated by full adders will not propagate to the next adder but to the next stage. To save the power, we are applying the gating technique to perform the second stage addition in the last stage only.

MSB positioned bits will not be added in the first stage of accumulation; instead, they will be added in the second. The R1, R2, and R3 values obtained in the previous stage are contributed to the partial product reduction stage's following stage. To prepare for final-stage addition, the MSB bits must be gathered in the second step.

Throughout the partial product reduction stage, designers compress the partial product matrix to 2 rows by using the Dadda tree representation. The main reason is because this partial product matrix is different from the typical partial product matrix. Also for partial product matrix, researchers expected that the Dadda tree alternative, as opposed to the Wallace tree multiplier approach, could even require less counters. We'll perform (2N-k-1) bit addition by diminishing Partial Product Matrix to two rows.

For unsigned bit, the highest significant bit was passed though the OR gate and AND gate. For signed bit, the highest significant bit was performed addition and it is subtracted with minus 1. Hence, a three row partial product matrix is also attained. In register accumulation, the three-row PPM is saved. The result is to form the next partial product matrix for the partial product generation process.

When the Partial Product Matrix is reduced to two rows, the column with the highest significance bit only produces two product names.

The outputs of this translation circuit was passed to the input of alpha-bit addition. The accumulation was done in the alpha-bit addition which is shown in Fig. 3. As a consequence, if we really need to get the final outcome by utilizing the activate signal. If the enable signal is high, it shows the final output.

III. METHODOLOGY

From the existing mac unit it can be observed that delay is more since for alpha bit addition a ripple carry adder is used and for multiplier dadda multiplier is used. Since the multipliers and adders are basic modules used in the MAC unit, the performance of these modules impact performance of MAC unit.

The proposed architecture has the following characteristic:

It minimizes the carry propagation chain by using the Wallace tree multiplier.

Instead of ripple carry adder in (k+∝-1)  bit addition parallel prefix adder is used for minimizing the delay.

Conclusion

In this paper, a novel two stage pipelined MAC unit is proposed. In this mac unit for the purpose of addition a parallel prefix adder and for the purpose of multiplication a Wallace tree multiplier is used to enhance the speed which is critical in MAC unit. Further various adder architectures we can use for the trade-offs among delay, area, and power. Additionally, by using different architectures in place of the multiplier and accumulator (adder), we are able to create a variety of MAC unit models.

References

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Copyright

Copyright © 2022 P. Samreen Aalia, K. Yogitha Bali. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.