Design and Implementation of a High-Performance 128-Bit Arithmetic Logic Unit Using Carry Look Ahead Adder, Vedic Multiplier, and Radix-2 Restoring Division
Keywords:
128-bit ALU, Carry look ahead adder, FPGA, Radix-2 restoring division, Urdhva Tiryakbhyam, Vedic multiplier, Verilog HDL, VLSI, Xilinx VivadoAbstract
This paper presents the design, Verilog HDL implementation, and simulation of a high-performance 128-bit Arithmetic Logic Unit (ALU) targeting advanced digital processing applications. The proposed architecture integrates three optimised arithmetic modules—a 128-bit hierarchical Carry Look Ahead (CLA) adder for fast addition and subtraction, a 128×128 Vedic multiplier based on the Urdhva Tiryakbhyam sutra for high-speed parallel multiplication, and a Radix-2 restoring division unit for accurate quotient and remainder computation. The ALU additionally supports six essential bitwise logical operations—AND, OR, XOR, NOT, NAND, and NOR—controlled through a 3-bit opcode-based selection unit. The complete design is modelled in Verilog HDL, simulated, and functionally verified using Xilinx Vivado on the Kintex-7 XC7K70T FPGA platform. Synthesis results indicate 95.04% LUT utilisation, 24.17% DSP48 block usage, and an estimated critical path delay of 30–50 ns. Simulation waveforms confirm the correct operation of all arithmetic and logical functions, including division remainder generation and division-by-zero detection. The proposed design demonstrates significant improvements in computational width, speed, and functional completeness over conventional 32/64-bit ALU architectures employing Ripple Carry Adders.
References
G. Nagaraju and G. V. S. Reddy, “Design and implementation of 128 × 128 bit multiplier by ancient mathematics,” International Journal of Engineering Research & Technology (IJERT), vol. 3, no. 9, pp. 1363–1366, Sep. 2014.
M. M. Mano and M. D. Ciletti, Digital design: With an introduction to Verilog HDL, 5th ed. Noida, India: Pearson Education India, 2013.
S. Ainaresh, “High speed carry look ahead adder-subtractor using Verilog,” GitHub Repository, 2022.
B. K. Tirthaji, Vedic mathematics. Delhi, India: Motilal Banarsidass Publishers, 2023.
S. G. Ziavras, "Versatile processor design for efficiency and high performance," Proceedings International Symposium on Parallel Architectures, Algorithms and Networks. I-SPAN 2000, Dallas, TX, USA, 2000, pp. 266-271
J. M. Rabaey, A. Chandrakasan, and B. Nikolic, Digital integrated circuits: A design perspective, 2nd ed. Upper Saddle River, NJ, USA: Prentice Hall, 2003.
P. M. Kogge and H. S. Stone, “A parallel algorithm for the efficient solution of a general class of recurrence equations,” in IEEE Transactions on Computers, vol. C-22, no. 8, pp. 786-793, Aug. 1973.
R. P. Brent and H. T. Kung, “A regular layout for parallel adders,” IEEE Transactions on Computers, vol. C-31, no. 3, pp. 260–264, Mar. 1982.
A. K. Verma and P. Ienne, “High-speed carry look-ahead adder design and implementation,” in Proc. IEEE Int. Conf. VLSI Design, 2010, pp. 421–426.
C. S. Wallace, “A suggestion for a fast multiplier,” IEEE Transactions on Electronic Computers, vol. EC-13, no. 1, pp. 14–17, Feb. 1964.
H. Thapliyal and M. B. Srinivas, “High-speed efficient N×N bit parallel hierarchical overlay multiplier architecture based on ancient Indian Vedic mathematics,” Transactions on Engineering, Computing and Technology, vol. 2, pp. 225–228, 2004.
K. Hwang, Computer Arithmetic: Principles, architecture and design. New York, NY, USA: Wiley, 1979.
J.-S. Chiang, H.-D. Chung, and M.-S. Tsai, “Carry-free radix-2 subtractive division algorithm and implementation of the divider,” Tamkang Journal of Science and Engineering, vol. 3, no. 4, pp. 249–255, 2000.
N. H. E. Weste and D. M. Harris, CMOS VLSI design: A circuits and systems perspective, 4th ed. Boston, MA, USA: Pearson, 2011.
S. Brown and Z. Vranesic, Fundamentals of digital logic with Verilog design, 3rd ed. New York, NY, USA: McGraw-Hill, 2014.