Linear-feedback Shift Registers (LFSRs) are pivotal components in digital circuitry, characterized by their ability to generate sequences based on a linear function of their previous states. This paper delves into the fundamental principles, applications, and advancements in LFSR technology. LFSRs find extensive use in creating pseudo-random sequences, which are crucial in various domains such as cryptography, communication, and probabilistic algorithms.

This study introduces a novel approach for implementing a programmable Infinite Impulse Response (IIR) filter by leveraging the Modified Karatsuba formula. The Karatsuba formula is renowned for its capability to accelerate large number multiplication by dividing operands into equal-length parts. Traditionally, multiplying two n-digit numbers demands O(n^2) elementary operations.

The continuous evolution of integrated circuits and their deployment in critical applications demand robust security mechanisms to safeguard sensitive data and intellectual property. Logic locking techniques have emerged as a prominent approach to protect circuits from unauthorized access and intellectual property theft. However, the increasing sophistication of attacks against these logic locking mechanisms necessitates innovative defenses.

This study delves into the realm of approximate computing, where computational errors and imprecisions are embraced as acceptable trade-offs to achieve more efficient and resource-conserving solutions. The research focuses on the design of approximate adders within the framework of Quantum-dot Cellular Automata (QCA), a promising technology for ultra-low-power computation.

User privacy and security issues in IoT devices have become a growing concern in recent years. This study aims to investigate these issues from a usability-centric perspective. The research method employed in this study includes a survey and user testing. The results indicate that while IoT systems offer convenience and efficiency, they also pose significant privacy and security risks to users.

With the continuous development of wearable technology, Chinese is increasingly widely used in the field of user health monitoring. This paper aims to explore the design and usability assessment of wearable technology and user health monitoring. Firstly, the development and application of wearable technology, including heart rate monitoring, sleep monitoring, exercise monitoring, and blood pressure monitoring.