Low Latency and Power Efficient Aproximate Multipliers using Compressors

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Low Latency and Power Efficient Aproximate Multipliers using Compressors

S. Sugunal

Assistant Professor,

Department of ECE, SVS College of Engineering, Coimbatore, Tamilnadu, India

R. Kiruthika2

2PG Scholar,

Department of ECE, SVS College of Engineering, Coimbatore, Tamilnadu, India

Abstract:- Approximate computing has been considered to improve the accuracy-performance trade-off in error- tolerant applications. For many of these applications, multiplication is a key arithmetic operation. Given that approximate compressors are a key element in the design of power-efficient approximate multipliers, we first propose an initial approximate 4:2 compressor that introduces a rather large error to the output. According to the mean relative error distance (MRED), the most accurate of the proposed 16×16 unsigned designs has a 44% smaller power-delay product (PDP) compared to other designs with comparable accuracy. The radix-4 signed Booth multiplier constructed using the proposed compressor achieves a 52% reduction in the PDP-MRED product compared to other approximate Booth multipliers with comparable accuracy. The proposed multipliers outperform other approximate designs in image sharpening and joint photographic experts group (JPEG) applications by achieving higher quality outputs with lower power consumptions.

Keywords: Approximate Computing, low-Power, low-area


    In applications like multimedia signal processing and data mining which can tolerate error, exact computing units are not always necessary. They can be replaced with their approximate counterparts. Research on approximate computing for error tolerant applications is on the rise. Adders and multipliers form the key components in these applications. In approximate full adders are proposed at transistor level and they are utilized in digital signal processing applications. Their proposed full adders are used in accumulation of partial products in multipliers. To reduce hardware complexity of multipliers, truncation is widely employed in fixed- width multiplier designs. Then a constant or vari-able correction term is added to compensate for the quantization error introduced by the truncated part. Approximation techniques in multipliers focus on accumulation of partial products, which is crucial in terms of power consumption. Broken array multiplier is implemented in, where the least significant bits of inputs are truncated, while forming partial products to reduce hardware complexity. The proposed multiplier in saves few adder circuits in partial product accumulation. In two designs of approximate 4-2 compressors are presented and used in partial product reduction tree of four variants of 8 × 8 Dadda

    multiplier. The major drawback of the proposed compressors in is that they give nonzero output for zero valued inputs, which largely affects the mean relative error (MRE) as discussed later. The approximate design proposed in this brief overcomes the existing drawback. This leads to better precision.


    Xilinx ISE (Integrated Software Environment) is a software tool produced by Xilinx for synthesis and analysis of HDL designs, enabling the developer to synthesize ("compile") their designs, perform timing analysis, examine RTL diagrams, simulate a design's reaction to different stimuli, and configure the target device with the programmer.

    The Web Edition is a free version of Xilinx ISE that can be downloaded at no charge. It provides synthesis and programming for a limited number of Xilinx devices. In particular, devices with a large number of I/O pins and large gate matrices are disabled. The proposed approximation is utilized in two variants of 16-bit multipliers. Synthesis results reveal that two proposed multipliers achieve power savings of 72% and 38%, respectively, compared to an exact multiplier. They have better precision when compared to existing approximate multipliers. Mean relative error figures are as low as 7.6% and 0.02% for the proposed approximate multipliers, which are better than the previous works.

    Performance of the proposed multipliers is evaluated with an image processing application, where one of the proposed models achieves the highest peak signal to noise ratio.

    Figure 1 A 7:3 counter and 6:3 counter built from full and half adders.

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    The 4:2 compressor design reduces the complexity of the Wallace tree structure for multiplication [1]. A 4:2 compressor has four inputs and two outputs i.e. the sum and the carry apart from a carry in (cin) and carry out (cout) [5,6,8,9,17,20]. Cin is the cout of the previous

    compressor and cout becomes the cin of the next compressor.

    Figure 3



      Figure 4


      Figure 5


    In this brief, a new binary counter based on a novel symmetric bit stacking approach is proposed. We showed that this counting method can be used to implement 6:3 and 7:3 counters, which can be used in any binary multiplier circuit to add the partial products. We demonstrated that 6:3 counters implemented with this bit stacking technique achieve higher speed than other higher order counter designs while reducing power consumption. This is due to the lack of XOR gates and multiplexers on the critical path. The 64-bit and 128-bit counter based Wallace tree multipliers built using the proposed 6:3 counters outperform both the standard Wallace tree implementation as well as multipliers built using existing 7:3 counters.


    I would like to thank KANNAN, SABARIGIRIRAJ for their support, services, and fruitful discussions.


  1. Mohammed Saeed Ansari, Honglan Jiang,Bruce F. Cockburn, and Han, Low-power approximate Multipliers using encoded partial products and approximate compressors, IEEE Transistion. Computer.-Aided Design Integrated Circuits System., volume 32, number. 1, page. 21563357, Jan. 2018.

  2. V. Gupta, D. Mohapatra, A. Raghunathan, and K. Roy, Low- power dig-ital signal processing using approximate adders, IEEE Transistion. Computer.-Aided Design Integrated Circuits System., volume 32, number. 1, page. 124137, Jan. 2013.

  3. K.-J. Cho, K.-C. Lee, J.-G. Chung, and K. K. Parhi, Design of low-error fixed-width modified booth multiplier, IEEE Trans. Very Large Scale Integr. (VLSI) System volume 12, number 5 , page 522 -531, May 2004

  4. H. R. Mahdiani, A. Ahmadi, S. M. Fakhraie, and C. Lucas, Bio-inspired imprecise computational blocks for efficient VLSI implementation of soft-computing applications, IEEE Trans. Circuits Syst. I, Reg. Papers, volume 5 number 4 page 862,April 2010

  5. A. Momeni, J. Han, P. Montuschi, and F. Lombardi, Design and analysis of approximate compressors for multiplication, IEEE Computing volume64 number 4 page 984 994 April 2015

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