ECE/CoE 0142 Computer Organization
ECE 0142 Computer Organization
Homework 2
Assigned: 1/19/2016 Due: 1/22/2016 before recitation
Name___________________________________________________________________
ID_____________________________________________________________________
1. (15 pts) Fill in the table. Write down all possible binary representations for the decimal values in the first column. Assume that you have 5 bits in total. If the number cannot be represented within 5 bits, write “not representable”.
|decimal |5-bit binary |
| |sign-magnitude |1’s complement |2’s complement |
|0 | | | |
|-1 | | | |
|-16 | | | |
| 16 | | | |
|-2.25 (use 2 digits for | | | |
|fractional part) | | | |
2. (6 pts) Show the steps in converting the following floating numbers into single-precision binaries according to the IEEE 754 standard.
-31.187510
s =
e =
f =
The single precision form is:
3. (6 pts) Show the steps in converting the following single-precision binaries according to the IEEE 754 standard into decimal FP number.
1 1000 0111 1010…02
s =
e =
f =
The decimal FP number is:
4. (6 pts) Show the negative value range of the IEEE 754 floating numbers, considering both normalized and un-normalized representations. Hint, this can be derived from the positive value range.
5. (10pts) IEEE 754 can represent same number of FPs between 2n and 2n+1 as 2n+1 and 2n+2. How many FP numbers can be represented in each such interval? Find out the difference between neighboring numbers for interval (2n , 2n+1). Can you infer from the results if IEEE 754 is better for small numbers or large numbers?
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