High-performance digital systems require efficient multipliers that can provide low area, low power, and high-speed operation. Traditional multiplier designs often face trade-offs between area, speed, and power consumption, impacting overall system efficiency. This study presents a novel compact multiplier architecture leveraging multiplexer-based full adders to optimize both area and speed. By replacing conventional adders with multiplexer-based full adders, the design achieves significant area reduction without compromising computational accuracy or performance. Through simulation and analysis, the proposed design demonstrates improved delay and reduced hardware complexity compared to traditional architectures. The results indicate that the multiplexer-based full adder is an effective approach for achieving compact, high-speed multipliers suited for advanced digital systems, including signal processing and low-power applications. This work offers valuable insights into optimizing multiplier circuits and highlights the potential of multiplexer-based components in VLSI design.

The demand for high-speed and efficient multipliers is crucial in modern digital systems, especially in applications such as image processing, cryptography, and digital signal processing, where multiplication is a fundamental operation. This paper presents the design and implementation of an efficient 64-bit Vedic multiplier using the Urdhva Tiryakbhyam algorithm, one of the fastest methods derived from ancient Vedic mathematics. The proposed design leverages the parallelism inherent in Vedic multiplication techniques to significantly reduce computation time and improve processing speed. Comparisons with conventional multipliers demonstrate that the Vedic approach achieves a marked increase in performance and efficiency. Simulation results confirm that the 64-bit Vedic multiplier outperforms standard multipliers in terms of speed, resource utilization, and power consumption, making it a suitable candidate for high-performance computing applications.

This article discusses the types of critical thinking, critical thinking in the preparation of future primary school teachers, and critical thinking is the concept of objective thinking, which combines various types of human intelligence.

The article explores the primary types of ceramic refractory materials, focusing on their properties and applications in high-temperature industrial processes. Key technological advancements in refractory manufacturing are discussed, with an emphasis on enhancing material strength, chemical resistance, and durability. The analysis highlights the specific characteristics of each refractory type, including fireclay, magnesite, corundum, and silicon carbide, and their utilization across various industries such as metallurgy, energy, and glass production. Modern production and modification methods for refractories are presented, aimed at improving thermal resistance and reducing the operational costs of equipment.

The article presents an overview of the theoretical and pedagogical foundations for developing the communicative competence of future teachers. The author also analyzes the content of the special subject "Communicative competence of a teacher" for developing the communicative competence of a future teacher.