Objective:
- To design a leading one detector with leading output and also log value.
- To remodified the Barrel left shifter with truncated variable method using leading detection. Here, the bit will be shifted left with number of zeros as per leading input.
- Instead of traditional adaptive adder using RCA & CLA, we introduced a Hybrid adaptive PPA adder with Brent kung and kogge stone adder.
- The truncated bits (t) and higher-order bits (h) are treated as variable parameters rather than fixed constants.
- The design of Hybrid adaptive addition done with two PPA adder, for LSB addition using with Brent Kung adder and the MSB addition using with Kogge stone adder. Here, this adder designed with 8-bit and 16-bit architecture.
- For log value addition in the top module architecture, this proposed work design with Brent kung adder.
- Finally, Antilogarithm function will decide the output with support of log(n)+1. It will have shifted the value from Adaptive Hybrid sum value, as per logarithmic function of X = 2^(log_ab) × Mantissa.
- Finally, we developed this work in Verilog HDL, and verified functionality in Modelsim, and synthesize using Xilinx Vertex-5 FPGA, and compared all the parameters in terms of LUT, Slice registers, delay and power.
Proposed Abstract:
Logarithmic multipliers are widely applied in digital signal processing, machine learning, cryptography, and imaging because they reduce multiplication into addition and shifting. Recent approximate designs such as the Adaptive Fault-tolerant approximate multiplier target deep neural network accelerators by optimizing fault tolerance with leading-one detection and mantissa truncation. While effective for DNN reliability, the Adaptive Fault-tolerant approximate multiplier introduces deterministic approximation errors, relies on a limited carry-lookahead adder and ripple adaptive adder, and mainly focuses on ASIC implementation without extensive FPGA exploration. To overcome these restrictions, we propose a hybrid logarithmic multiplier that employs variable truncated (t) and variable higher-order (h) shifting methods with an adaptive parallel prefix adder (PPA). A leading-one detector is designed to generate both the position and the logarithmic value directly, and reducing redundant computations. The barrel shifter is remodified with adaptive truncation, which lowers area and delay. In Addition is performed by a hybrid PPA where Brent-Kung is used for least significant bits and Kogge-Stone for most significant bits, its achieving higher speed and balanced area efficiency compared to traditional ripple or CLA-based adders. Here, truncated and higher-order bits as variable parameters, which enables flexible precision control and more accurate error management across various applications. A compact Brent-Kung adder is also used for logarithmic value addition, while the antilogarithm unit reconstructs results adaptively with log(n)+1 shifting for accuracy and efficiency. The novelty of this design lies in integrating hybrid PPA adders with variable truncated and higher-order shifting, making it more reliable and versatile than existing approximate approaches such as the Adaptive Fault-tolerant approximate multiplier. This architecture is implemented in Verilog HDL, verified on ModelSim, and synthesized on Xilinx Virtex-5 FPGA. Performance is evaluated in terms of LUTs, slice registers, delay, and power, showing improvements over conventional approximate multipliers and ensuring suitability for DSP, AI, and real-time embedded systems.
Software Implementation:
- Modelsim
- Xilinx
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Hybrid Logarithmic Multiplier Using Variable Truncated (t) and Variable Higher Order (h) Shifting Method Using Adaptive PPA Adder
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