Two Novel Approximate Radix-4 Booth Encoders for Efficient Signed Approximate Booth Multipliers

In this paper, two approximate Radix-4 Booth encoders AR4BE1 and AR4BE2 (Approximate Radix-4 Booth Encoder1, 2) are proposed to achieve great accuracy-cost trade-off, and a series of signed approximation multipliers (SAMs) are designed based on a hybrid coding approach, where the most significant bits (MSB) use exact radix-4 encoder, and the least significant bits (LSB) use the proposed AR4BE1 and AR4BE2. And a simple error compensation circuit is used to reduce the accuracy loss in partial product array reduction. The proposed SAMs can be reconfigured for different applications with different accuracy-cost trade-off requirement. We comprehensively evaluate the SAMs with respect to both hardware implementation and error analysis. Compared to the exact multiplier, the highest accuracy multiplier H10M6L0, has 22.8%, 32.1%, and 18.4% reduction in area, power consumption, and delay, respectively. The case study for image edge detection also proves the validity of the proposed SAMs in error-tolerant application.