Question

What is the primary reason that addition and subtraction are considered more complex than multiplication and division with floating-point representations?

What are subnormal numbers, and how do subnormal numbers help reduce the impact of underflow?

Answer 1

Addition and Subtraction are consoderably complex than multiplication in floating poing representaion because of the need to allign the Mantissas, whereas in multiplcation it is not necesssary for the digits to be aligned. The algorithm for it goes as follows

• Check for zeros
• Align significands (adjusting exponents)
• Add or subtract significands
• Normalize result

Subnormal numbers, once known as denormal numbers in floating-point writing, fill the underflow hole around zero in floating-point math. Subnormal qualities are an extraordinary class of floating-point esteems that are excessively near 0.0 to be spoken to as a standardized worth. The main significand (mantissa) of a subnormal number is zero. While including and taking away floating-point numbers, subnormal numbers forestall underflow.

Utilizing subnormal numbers gives exactness past the ordinary portrayal by utilizing driving zeros in the significand to speak to more modest qualities after the portrayal arrives at the base example. As the worth methodologies 0.0, you compromise accuracy for broadened range. Subnormal numbers are helpful if your application requires additional reach.

In any case, in a constant framework, utilizing subnormal numbers can drastically build execution idleness, bringing about unnecessary plan edges and continuous invades. On the off chance that the reproduction or created code performs estimations that deliver or devour subnormal numbers, the execution of these computations can be up to multiple times more slow than comparative figurings on typical numbers. The genuine reenactment or code execution time for subnormal number figurings relies upon your PC working climate. Commonly, for work area processors, the execution time for subnormal number estimations is multiple times more slow than comparable figurings on typical numbers.