IEEE 754 Floating Point Standard

The need for a standard

Across the lessons in this chapter, we have built on the rules of our $8$-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 $3$ bits and the exponent had $4$. In reality, the $8$-bit representation is just a toy example we used to illustrate some key concepts.

In the real world, computers use $32$ and $64$ 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 $0$.

In the rest of this lesson we will go through the conventions of the IEEE 754 format one by one.