Approximate multipliers attract a large interest in the scientific literature that proposes several circuits built with approximate 4-2 compressors. Due to the large number of proposed solutions, the designer who wishes to use an approximate 4-2 compressor is faced with the problem of selecting the right topology. In this paper, we present a comprehensive survey and comparison of approximate 4-2 compressors previously proposed in literature. We present also a novel approximate compressor, so that a total of twelve different approximate 4-2 compressors are analyzed. The investigated circuits are employed to design 8x 8 and 16x 16 multipliers, implemented in 28nm CMOS technology. For each operand size we analyze two multiplier configurations, with different levels of approximations, both signed and unsigned. Our study highlights that there is no unique winning approximate compressor topology since the best solution depends on the required precision, on the signedness of the multiplier and on the considered error metric.

Approximate multipliers are used in error-tolerant applications, sacrificing the accuracy of results to minimize power or delay. In this paper we investigate approximate multipliers using static segmentation. In these circuits a set of $m$ contiguous bits (a segment of $m$ bits) is extracted from each of the two $n$ -bits operand, the two segments are in input to a small $m\times m$ internal multiplier whose output is suitably shifted to obtain the result. We investigate both signed and unsigned multipliers, and for the latter we propose a new segmentation approach. We also present simple and effective correction techniques that can significantly reduce the approximation error with reduced hardware costs. We perform a detailed comparison with previously proposed approximate multipliers, considering a hardware implementation in 28 nm technology. The comparison shows that static segmented multipliers with the proposed correction technique have the desirable characteristic of being on (or close to) the Pareto-optimal frontier for both power vs normalized mean error distance and power vs mean relative error distance trade-off plots. These multipliers, therefore, are promising candidates for applications where their error performance is acceptable. This is confirmed by the results obtained for image processing and image classification applications.

Approximate computing is a technique that sacrifices the accuracy of the result for an advantage in terms of power, area, and speed. It is useful for error-tolerant applications such as image and video processing. Many approximate arithmetic circuits can be devised using approximate versions of the basic binary full adder that simply adds three bits to generate carry and sum. Therefore, the approximate full adder has been the subject of extensive investigation in recent years. In this paper we present a comprehensive analysis of approximate full adders, by synthesizing in a FinFET 14 nm technology the whole set of possible designs, achievable by modifying one or more entries of the full adder truth-table. Our exhaustive analysis shows that only a few out of the many thousands of synthesized circuits perform reasonably well as approximate full adders. Our analysis re-discovers the approximate full adders already proposed in the literature and identifies some new ones. Examples of using the newly discovered approximate full adders in typical error resilient applications are provided, showing the performance and the usefulness of approximate arithmetic circuit designs in the real-world.

In this paper we investigate a novel approximate multiply-and-accumulate (MAC) unit, that computes Y = A×B+C using static segmentation. The proposed architecture uses a unique carry-propagate adder and performs segmentation on the three operands A, B, and C, to reduce hardware cost. The circuit can be configured at design-time by two parameters. The first one controls the segmentation on A and B, while the second one controls the segmentation on C and the adder length. An error compensation technique is also employed, to reduce the approximation error. Error analysis and implementation results in 28nm CMOS for 8-bits multiplier with 20-bits and 24-bits addition are presented. The proposed approximate MACs outperform the state of the art, showing the largest power saving when the mean relative error distance (MRED) is larger than 2×10 ⁻³ and 4×10 ^-5 for 20 and 24-bits addition, respectively. For MRED of about 6×10 ⁻³ the proposed approximate MAC with 20-bits addition exhibits a power reduction larger than 60% compared to the exact MAC and larger than 27% compared to the state-of-the-art approximate MACs. Application examples to image filtering and template matching show that proposed approximate circuits are good candidates in applications where their error performances are acceptable.

In this paper a novel low-power approximate floating-point multiplier is presented. Since the mantissa computation is responsible for the largest part of the power consumption, we apply a novel approximation technique to mantissa multiplication, based on static segmentation. In our approach, the inputs of the mantissa multiplier are properly segmented so that a small inner multiplier can be used to calculate the output, with beneficial impact on power and area. To further improve performance, we introduce a novel segmentation-and-truncation approach which allows us to eliminate the shifter normally present at the output of the segmented multiplier. In addition, a simple compensation term for reducing approximation error is employed. The accuracy of the circuit can be tailored at the design time, by acting on a single parameter. The proposed approximate floating-point multiplier is compared with the state-of-the-art, showing good performance in terms of both precision and hardware saving. For single-precision floating-point format, the obtained NMED is in the range 10⁻⁵–7 × 10⁻⁷, while MRED is in the range 3 × 10⁻³–1.7 × 10⁻⁴. Synthesis results in 28 nm CMOS show area and power saving of up to 82% and 85%, respectively, compared to the exact floating-point multiplier. Image processing applications confirm the expectations, with results very close to the exact case.

In this paper, a novel implementation is proposed for the Delayed LMS (DLMS) filter, able to reduce the power dissipation while preserving regime performances. The approach relies on the observation that the error signal is small in magnitude and oscillates around zero when the circuit is close to the convergence point. Therefore, the most significant bits of the error signal continuously toggle from positive to negative values causing high switching activity in the multipliers of the feedback section. This paper proposes to employ a sign-modulus representation of the error signal, to substantially reduce the switching activity of the feedback path of the filter. Additional approximation techniques are also devised to further reduce power dissipation. Comparisons with the state-of-the-art show that the proposed filter is the only one able to approach the MSE of the exact implementation with a remarkable reduction of power dissipation. A test-chip in TSMC 28nm CMOS technology has been realized to experimentally verify the validity of our technique. The experimental results show the possibility of saving up to 45.4% of power consumption with respect to the exact implementation of the filter.