Question

Hello, I've been stuck on this problem for my assembly language class for awhile and would like some assistance. If you could show work so I know what is actually going on and can learn off you doing the problem that would be great. And if you could tell me what the difference between double and single precision that would be great also

Determine the decimal value that gives 42ACD000 in hex when represented in IEEE 754-1985 single precision.

CAUTION:

You will earn NO CREDITS if you simply show the final result.

You will incur penalty for not clearly showing work on how results of intermediate steps are obtained.

Answer 1

So basically as we are talking about IEEE 754-1985( 1985 because it was invented in that year) single precision format so let me tell you it is a binary computing format that occupies 4 bytes (fixed) in computer memory. Now it is called as IEEE 754-2008.

So as we have our Hex number so first we have to convert our Hex number to decimal and then we convert it into binary ( we can convert hex directly to binary but it is mentioned in your question that it is represented in decimal) and then we will convert it into single precision.

Conversion of Hex to Decimal

so the method is basically you have to multiply every digit in number from 16(Because Hex number has a base of 16) and some power (power depends on the place of digit).

just look at the image you will understand.

now we have our decimal number but to convert it into single precision we have to convert it into binary number also so for that i have another image for you.

Now we will convert it into single precision floating point (i.e IEEE-753 1985)

And You asked about single and double precision the only difference is that single precision deals with 32 bit floating numbers and double precision deals with 64 bit numbers ( in double precision we will make 16 pairs in the end as we made 8 pairs in single precision).

I hope i answered your question well because it took a lot of work from my side too.

Thank you