👉 Hardware math, also known as digital arithmetic, is the foundation of how computers perform mathematical operations. It involves representing numbers and performing calculations using binary (base-2) systems, where each digit is a binary digit (bit), either 0 or 1. Basic operations like addition, subtraction, multiplication, and division are implemented through specific algorithms optimized for hardware execution. For instance, addition is typically performed using a carry mechanism, where bits are added and carried over as needed, while multiplication often involves repeated addition. Specialized circuits, such as adders and multipliers, are designed to handle these operations efficiently. Additionally, hardware math includes floating-point arithmetic for handling real numbers, which involves representing numbers in a format that includes a significand (mantissa) and an exponent, allowing for precise calculations of very large or very small numbers. This efficient and optimized hardware math enables computers to perform complex mathematical tasks at high speeds, essential for applications ranging from scientific simulations to machine learning.
