# MCS-284 Chapter 4 Homework (Fall 2000)

When turning in a homework problem, if it is one from the book, you should indicate the exercise number. If it is not from the book, you should indicate the number I give with an x in it, as in 4.x1 and 4.x2 below. These will be the reference numbers I use in reporting back your standing on the homework.

Note that we are covering chapter 4 in two chunks at different points in the syllabus. You'll be able to do the first two problems from the earlier chapter 4 material, but problem 4.x2 will need to wait for the later material.

• Problem 4.x1: Consider taking the mirror image of a binary numeral, in the sense of reversing the left-to-right order of the bits. For example, the mirror image of 01100 is 00110. What binary numeral(s) have the property that taking the mirror image produces the same result as negating the numeral (using two's-complement)? Justify your answer: not only why the numeral(s) you list have this property, but also why you are sure than no others do.

• Do exercise 4.21 on pages 325-326.

• Problem 4.x2: Write the 32 bits for the floating point number that results from multiplying by two the floating point number
```0000 0110 0010 0111 0000 0000 0000 0000
```
(Note that this is divided into chunks of four bits just to help you count positions more accurately. The chunks do not correspond to the logically significant portions of the representation.) Be sure to explain how you arrived at your answer.

Instructor: Max Hailperin