Problem 1: Reason It Out (15pts)

So, grab your calculator program and plug this stuff in and convert. I'm not taking time to give you detailed explanations of stuff that you all learned in 250, or even some math class in a galaxy far, far away. Oh, and please reread the directions for this problem. I stated in class repeatedly, and in the instructions, that powers of two or powers of 16 were acceptable answers. Some of you can't do anything without a calculator, and I can't allow calculators because if you are smart enough to graduate with a CS degree from UMCP, you are smart enough to figure out how to program information into all but the most basic calculator-and I'm not supplying the class with such things.

So, I provide you with an alternative-just show me your answer in an intermediate format-still technically base 10, but in a way that also makes it clear how well you understand the concepts we are actually testing, not whether or not you can do arithmetic by hand.

This policy will be in effect throughout the course; so, don't waste time doing work that will earn you no points-and is guaranteed to lose you points because you need the time that you are wasting to answer other questions on the exams.

1. The 20-bit unsigned binary number     0xF2D41 is:

   
   

   $$1 \; + \;4 * 16 \;+\; 13 * 16^{2} \;+\; 2 * 16^3 \;+\; 15 * 16^4$$
   
   

2. The 20-bit sign magnitude binary number     0xF2D41 is:

   
   

   $$-( 1 \; + \;4 * 16 \;+\; 13 * 16^{2} \;+\; 2 * 16^3 \;+\; 7 * 16^4)$$
   
   

3. The 20-bit 2's complement number     0xF2D41 is:

   
   

   $$- (15 \;+\; 11 * 16 \;+\; 2* 16^2 \;+\; 13* 16^3)= -(0x0D2BF) = -( 0x0D2BE \;+\; 1)$$
   
   

4. The 20-bit unsigned binary number     ~0 is is 0xFFFFF = $2^{20}-1$.

5. The 20-bit 2's complement number      1 << 19 is 0x80000 , or $2^{19}= 8 * 16^4$