> For the complete documentation index, see [llms.txt](https://valineliu.gitbook.io/deuterium-wiki/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://valineliu.gitbook.io/deuterium-wiki/reading/cs-jing-dian-shu-ji/csapp-3e-homework-solution/2.-representing-and-manipulating-information/2.86-extend-precision.md).

# 2.86 Extend Precision

★

**Problem**:

Intel-compatible processors also support an "extended-precision" floating-point format with an 80-bit word divided into a sign bit, k=15 exponent bits, a single integer bit, and n=63 fraction bits. The integer bit is an explicit copy of the implied bit in the IEEE floating-point representation. That is, it equals 1 for normalized values and 0 for denormalized values. Fill in the following table giving the approximate values of some "interesting" numbers in this format:

| Desc                           | Extended Value            | Extended Decimal |
| ------------------------------ | ------------------------- | ---------------- |
| Smallest positive denormalized | 0 00...(15) 0 00...(62)1  | 2^(-4145)        |
| Smallest positive normalized   | 0 00...(14)1 1 00...(63)  | 2^(-4082)        |
| Largest normalized             | 0 11...(14)0 1 111...(63) | 4083\*(2-2^-63)  |