Energy efficient multiply-accumulate unit using novel recursive multiplication for error-tolerant applications

Abstract

The primary requirement for multimedia applications is energy efficient design along with computational efficiency of portable devices. This work proposes an energy efficient MAC with error compensating novel approximate adder and approximate multiplier. The proposed approximate hierarchical adder (AXHA – N) has the advantage of zero carry propagation and consists of only two gate levels which deliver very high speed and very low energy consumption along with the near to zero mean error distances. The proposed approximate 4 - bit multiplier also has no carry propagation from Least Significant Bit (LSB) to Most Significant Bit (MSB), which leads to high speed with very low energy consumption and acceptable error profiles. Higher bit size multipliers can be built using the proposed modified recursive multiplication scheme. This work proposes three variants AXMAC1, AXMAC2, AXMAC3 basing on one or both of adder and multiplier being approximate. The proposed AXMAC3 with any k, has energy savings ranging from 40% to 60% for different AxL when compared to accurate with Mean Error Distance between −358 and 4305. The MED for AXMAC3 with k=8, AXL=4 is only 0.7% of the maximum possible value with 60% energy savings. The MED for AXMAC3 with k=12s, AXL=4 is only 0.8% of the maximum possible value with 57% energy savings. Mean Relative Error Distance (MRED) and Normalised Mean Error Distance (NMED) are also evaluated and presented in the paper for wholesome evaluation of AXMAC. The (Energy savings, MRED, MED) tuple 8−bit MAC for design of Adams et al., (2019) with k=8 is (26.9%, 0.1, −15048), for proposed AXMAC3 with similar configuration has (57%, 0.01, 3663).