IEEE Standard $754$ Encoding Scheme with smaller w

Creating smaller hypothetical floating$-$point representations based on the IEEE floating point format allows us to investigate this encoding scheme more easily, since the numbers are easier to compute and manipulate.

Download the A$2\_$Q$2\_$Table.pdf or A$2\_$Q$2\_$Table.docx from our course web site $($under Assignment $2)$ and open the file with the format you would like to work with: pdf or Word.

The table lists several fractional decimal numbers represented as $6-$bit IEEE$-$like floating point numbers $($w $=6).$ The format of these $6-$bit floating$-$point numbers is as follows:

$-$ One $(1)$ bit is used to express for the sign $($s$),-$ Three $(3)$ bits are used to express exp $($k $=3),-$ Two $(2)$ bits are used to represent frac $($n $=2),-$ in the following order: s exp frac.

Complete the table $($the same way as in Figure $2\mathrm{.}35$ in our textbook$),$ i$.$e$.,$ fill in the white table cells then answer the following eleven $(11)$ questions Q$2$ b$.$ to Q$2$ l$.$ below.

Tip: Have a look at Figure $2\mathrm{.}35$ in our textbook, which illustrates a similar table for a hypothetical $8-$bit IEEE$-$like floating$-$point format. This will give you an idea of how to complete the table. Also, Figure $2\mathrm{.}34$ displays the complete range of these $6-$bit IEEE$-$like floating point numbers as well as their values between $-1\mathrm{.}0$ and $1\mathrm{.}0.$ This diagram may be helpful when you are checking your work.