rcgldr said:The fractional (mantissa) part of the number with the lower exponent is shifted to the right before addition is performed. This results in truncation error.
Floating point addition is a mathematical operation used in computing, specifically for performing calculations with numbers that have a fractional component. It is commonly used in scientific and engineering applications where precision is important.
Floating point addition works by converting numbers into a standardized format, where the fractional portion is represented by a binary number and the whole number portion is represented separately. The numbers are then added together using a predetermined algorithm, taking into account the exponents and rounding to maintain accuracy.
Floating point addition in hardware is typically performed by specialized processors, known as floating point units (FPUs), which are designed specifically for this task. In contrast, floating point addition in software is performed by the computer's central processing unit (CPU), which is a more general-purpose processor. This can result in differences in speed and accuracy.
One common issue with floating point addition is the limited precision of floating point numbers, which can result in rounding errors and inaccuracies. Another issue is the potential for overflow or underflow, which occurs when the result of an addition operation is too large or too small to be represented accurately.
Floating point addition can be optimized for speed by using specialized hardware, such as FPUs, which are designed to perform these operations quickly and efficiently. Additionally, algorithms and programming techniques can be used to minimize the number of operations needed and reduce the likelihood of overflow or underflow.