22UEL031 · Research Project Phase II · April 2026

Adaptive Dual-Radix
Precision Systolic Array

An energy-aware machine learning accelerator architecture combining Radix-8 Booth encoding with a Radix-4 Adder to deliver 45.97% delay reduction and 14.81% power savings over conventional systolic designs.

Institution
Avinashilingam Institute
Department
ECE · School of Engineering
Mentor
Mrs. S. Manjulambigai
Tools
Verilog · ModelSim · Xilinx ISE
Explore Project ↓ View Results GitHub ↗
PG
Priyanka Gandhi A
22UEL031
Lead
MJ
Mrs. S. Manjulambigai
M.E. · Asst. Professor, ECE
Mentor
GL
Gopika P L
22UEL010
Teammate
SM
Supriya M
22UEL045
Teammate
ST
Shalini T
22UEL050
Teammate

01

Introduction

Machine Learning algorithms demand efficient, high-speed hardware for real-time inference and training. Systolic Arrays (SAs) have become the architecture of choice in ML accelerators — including Google's TPU — owing to their inherent data parallelism and regular structure.

Conventional systolic arrays suffer from high critical-path delay, excessive area complexity, and high dynamic power consumption — bottlenecks that this project directly addresses through dual-radix factorization.

High Delay
Carry propagation through multiple CPA stages creates long critical paths that limit operating frequency.
📐
Area Complexity
Repeated instantiation of large multiplier and adder circuits across the array inflates gate count and silicon area.
Power Drain
High dynamic power from redundant switching activity across PE stages makes scaling energy-inefficient.

02

Objectives

Six concrete design goals drive the ADR-SA architecture.

01
Design a factored systolic array architecture using Radix-8 Booth multiplication and a Radix-4 Adder for machine learning acceleration.
02
Reduce critical path delay and improve computation speed compared to conventional CPA-based systolic arrays.
03
Minimize power consumption and silicon area through early carry generation and compressed adder logic.
04
Overcome inefficiencies of conventional multiplier architectures including radix-2, radix-4, and standard CPA designs.
05
Support real-time ML applications such as image processing, NLP, and video compression.
06
Demonstrate scalable performance with a 3×3 ADR-SA verified via ModelSim functional simulation.

03 / 04

Literature Survey

A comprehensive review of ten significant works in systolic array design and ML accelerator optimization was conducted across IEEE TVLSI, IEEE TCAS-II, ACM/IEEE DAC, and other leading venues.

# Author(s) Year Venue Key Contribution
01K. Inayat, I. Ullah, J. Chung2024IEEE TVLSIRadix-8 factored SA for ML — significantly improves area, power, and delay over conventional SAs in resource-constrained environments.
02H. Lee, J. Park, S. Kang2024IEEE TVLSIArea-efficient redundancy for systolic arrays — high fault coverage and low area overhead for dependable edge AI accelerators.
03M. A. Shafique, K. Inayat, J. A. Lee2023HEART Symp.CSA-based radix-4 Gemmini SA — higher speed, lower latency, and better energy efficiency with minimal area overhead.
04K. Inayat, J. Chung2022IEEE TVLSIHybrid accumulator FSA — improved throughput and energy efficiency over standard systolic designs.
05H. Waris, C. Wang, W. Liu, F. Lombardi2021IEEE TCAS-IIApproximate radix-8 Booth multipliers for FPGA — significant delay and energy improvements with minimal accuracy loss.
06K. Inayat, J. Chung2021ElectronicsCPA-factored Gemmini SA — reduces latency and energy usage in ML acceleration hardware.
07I. Ullah, K. Inayat, J.-S. Yang, J. Chung2020ACM/IEEE DACRadix-8 factored SA for tensor processing — higher throughput and lower arithmetic redundancy in tensor operations.
08Z.-G. Liu, P. N. Whatmough, M. Mattina2020IEEE CALSystolic tensor array with structured sparsity — enhances inference speed and reduces power for mobile AI systems.
09S. Ryu, N. Park, J.-J. Kim2019IEEE TVLSIFeedforward-cutset-free pipelined MAC — higher speed, lower latency, better energy efficiency for ML accelerators.
10A. A. Del Barrio, R. Hermida2017DATE Conf.Slack-based deployment of radix-8 Booth multipliers — minimizes area and critical path delay while maintaining performance.

05

Proposed Method

The ADR-SA extracts Booth encoding and hard-multiple generation from individual Processing Elements and shares them at the input stage. The Radix-4 Adder replaces the conventional CPA in the accumulation stage.

ADR-SA Data Flow
IN
Input Data
8-bit operands
HCP
Hard Multiple
Carry Portioned FSA
R8
Radix-8 Booth
Encoding
PP
Partial Products
Wallace Tree
PE
Processing Element
3×3 array
R4A
Radix-4 Adder
Final accumulation
OUT
Output
16-bit result

Booth Encoding: Radix-4 vs Radix-8

Conventional
Radix-4 Booth Encoding
Groups bits in sets of 3 — generates ~n/2 partial products. Selects from {0, ±X, ±2X}.
Y(i+1)Y(i)Y(i−1)MiOperation
00000X
001+1+1X
010+1+1X
011+2+2X
100−2−2X
101−1−1X
110−1−1X
11100X
✦ Proposed
Radix-8 Booth Encoding
Groups bits in sets of 4 — generates ~n/3 partial products. Selects from {0, ±X, ±2X, ±3X, ±4X}.
ABCDOperation
00000X
0001+1X
0011+2X
0101+3X
0111+4X
1000−4X
1010−3X
1110−1X

Radix-4 Adder (RD4A) — Boolean Equations

The RD4A processes two bits simultaneously, reducing propagation delay and power versus a traditional binary adder. It has 5 inputs (Cin, Ai, Ai+1, Bi, Bi+1) and 3 outputs (Cout, Sumi, Sumi+1).

Boolean Output Equations
Cout = Ai+1·Bi+1 + (Ai·Bi)(Ai+1 + Bi+1) + Cin·((Ai + Bi)(Ai+1 + Bi+1))
Sumi+1 = (Ai+1 ⊕ Bi+1) ⊕ (Ai·Bi + Cin·Ai + Cin·Bi)
Sumi = (Ai ⊕ Bi) ⊕ Cin

06

Results & Discussion

All synthesis results obtained under identical Xilinx ISE conditions — Speed Grade: −7, 8-bit operands, same device target.

45.97%
Delay Reduction
8.800 ns → 4.755 ns
210 MHz
Frequency Gain
Up from 113.636 MHz (1.85×)
14.81%
Power Savings
243 mW → 207 mW
11.11%
Area Reduction
1916 → 1703 gates

CPA vs CSA vs Radix-4 Adder — Xilinx ISE Synthesis

Metric CPA (Carry Propagate) CSA (Carry Select) Radix-4 Adder Best
Area (Gates) 1916 1988 (+3.76%) 1703 (−11.11%) Radix-4
Power (mW) 243 223 (−8.23%) 207 (−14.81%) Radix-4
Delay (ns) 8.800 8.696 (−1.18%) 4.755 (−45.97%) Radix-4
Max Freq (MHz) 113.636 ~115 210.305✦ Best Radix-4
4-Input LUTs 275 222 Radix-4

3×3 ADR-SA Array — Verified PE Outputs

The 3×3 ADR-SA was implemented and verified in ModelSim. Data moves sequentially from one PE to the next with synchronized computation. Power rises linearly (not exponentially), confirming linear scalability.

PE 1,1
30
PE 1,2
36
PE 1,3
42
PE 2,1
66
PE 2,2
81
PE 2,3
96
PE 3,1
102
PE 3,2
126
PE 3,3
150

07

Conclusion

The ADR-SA integrates two complementary optimizations — Radix-8 Booth encoding and a Radix-4 Adder — to simultaneously address the three core bottlenecks of conventional systolic arrays. The result is a balanced, scalable architecture validated under identical Xilinx ISE synthesis conditions.

−11.11%
Area Reduction
1916 → 1703 equivalent gates
−14.81%
Power Reduction
243 mW → 207 mW total power
−45.97%
Delay Reduction
8.800 ns → 4.755 ns critical path
+85%
Frequency Gain
113.6 MHz → 210.3 MHz max clock

The 3×3 ADR-SA array-level simulation confirms functional correctness and linear scalability, making the ADR-SA a strong candidate for energy-constrained ML accelerators in edge computing, image processing, NLP, and video compression applications.


07.5

Publication

Presented at the National Conference on Sustainable Engineering Research & Applications (NCSERA-2026), Feb 26–27, 2026, organized by Avinashilingam Institute for Home Science and Higher Education for Women, Coimbatore.

Certificate of Presentation

Certificate of Presentation
Priyanka Gandhi A
NCSERA‑2026 · Feb 26–27, 2026

Paper titled "Adaptive Dual-Radix Precision Systolic Architecture for Energy-Aware Machine Learning Acceleration" presented by Priyanka Gandhi A, Dept. of ECE, School of Engineering, Avinashilingam Institute, under the track Sustainable Biomedical Devices and Communication Technologies.

Project Timeline

Aug – Oct 2025
Literature Survey
Reviewed 10 key papers on systolic arrays, Radix-8 Booth multipliers, and ML accelerator adders across IEEE TVLSI, DAC, TCAS-II.
Oct – Dec 2025
Architecture Design
Designed the Factored Radix-8 Systolic Array with Hard-Multiple Carry Portioned (HCP) FSA and evaluated Carry Select Adder vs Radix-4 Adder for the accumulation stage.
Dec 2025 – Jan 2026
Verilog Implementation & Simulation
Coded the full 3×3 ADR-SA in Verilog HDL. Verified MAC operation and 3×3 systolic array outputs via ModelSim functional simulation.
Jan – Feb 2026
Synthesis & Analysis
Synthesized on Xilinx ISE. Compared CPA, CSA, and Radix-4 Adder on area (gates), power (mW), and delay (ns) under identical conditions.
Feb 26–27, 2026
NCSERA-2026 Conference Presentation
Paper presented at the National Conference on Sustainable Engineering Research & Applications, Avinashilingam Institute, Coimbatore.
Apr 2026
Project Report Submission
Final B.E. project report submitted in partial fulfillment of the degree in Electronics and Communication Engineering.

08

References

1
K. Inayat, I. Ullah, and J. Chung, "Factored systolic arrays based on radix-8 multiplication for machine learning acceleration," IEEE Trans. VLSI Syst., vol. 32, no. 7, pp. 1205–1215, Jul. 2024.
2
H. Lee, J. Park, and S. Kang, "An area-efficient systolic array redundancy architecture for reliable AI accelerator," IEEE Trans. VLSI Syst., vol. 32, no. 10, pp. 1950–1954, Oct. 2024.
3
M. A. Shafique, K. Inayat, and J. A. Lee, "CSA based radix-4 Gemmini systolic array for machine learning applications," in Proc. HEART, 2023, pp. 93–99.
4
K. Inayat and J. Chung, "Hybrid accumulator factored systolic array for machine learning acceleration," IEEE Trans. VLSI Syst., vol. 30, no. 7, pp. 881–892, Jul. 2022.
5
H. Waris, C. Wang, W. Liu, and F. Lombardi, "AxBMs: Approximate radix-8 Booth multipliers for high-performance FPGA-based accelerators," IEEE Trans. Circuits Syst. II, vol. 68, no. 5, pp. 1566–1570, May 2021.
6
K. Inayat and J. Chung, "Carry-propagation-adder-factored Gemmini systolic array for machine learning acceleration," Electronics, vol. 10, no. 6, p. 652, Mar. 2021.
7
I. Ullah, K. Inayat, J.-S. Yang, and J. Chung, "Factored radix-8 systolic array for tensor processing," in Proc. 57th ACM/IEEE DAC, 2020, pp. 1–6.
8
Z.-G. Liu, P. N. Whatmough, and M. Mattina, "Systolic tensor array: An efficient structured-sparse GEMM accelerator for mobile CNN inference," IEEE Comput. Archit. Lett., vol. 19, no. 1, pp. 34–37, Jun. 2020.
9
S. Ryu, N. Park, and J.-J. Kim, "Feedforward-cutset-free pipelined multiply-accumulate unit for the machine learning accelerator," IEEE Trans. VLSI Syst., vol. 27, no. 1, pp. 138–146, Jan. 2019.
10
A. A. Del Barrio and R. Hermida, "A slack-based approach to efficiently deploy radix 8 Booth multipliers," in Proc. DATE, Mar. 2017, pp. 1153–1158.

09

Systolic Array — Data Flow Animation

Watch data tokens propagate through the 3×3 PE grid in real-time, synchronized to the clock edge.

Verilog HDL — Processing Element (PE)


10

Adder Performance Comparison

Animated bars show the relative performance of CPA, CSA, and Radix-4 Adder across all three metrics.

Delay (ns) — lower is better

CPA
8.800
CSA
8.696
Radix-4
4.755 ✦

Power (mW) — lower is better

CPA
243
CSA
223
Radix-4
207 ✦

Area (gates) — lower is better

CPA
1916
CSA
1988
Radix-4
1703 ✦