IEEE 754 Floating Point Standard
Explore the IEEE 754 floating point standard to understand how computers represent fractional numbers. Learn about denormalized numbers, special values like infinity and NaN, and the differences between single and double precision formats. This lesson clarifies standardized conventions crucial for accurate floating point computation.
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The need for a standard
Across the lessons in this chapter, we have built on the rules of our -bit floating point representation. However, we made our choices arbitrarily or based on convention. We could have just as easily decided that the mantissa had bits and the exponent had . In reality, the -bit representation is just a toy example we used to illustrate some key concepts.
In the real world, computers use and bit floating points, and there’s a myriad of ways the floating point conventions could be developed for each.
It makes sense then that a standard convention would be developed for all computer manufacturers to follow. This is exactly what the IEEE 754 Floating Point Standard is.
Another reason we need a standard is that we need conventions to represent numbers that are not included in the floating point representation we have developed so far. This includes small numbers and ...