CS 107 Assignment: data representation

1. For each of the following positive binary integers, what is the decimal (base ten) equivalent?

   • 1101
   • 1010111
   • 1

2. The number 1.398 is equal to 1 + 3/10 + 9/100 + 8/1000. If we move to binary, and use a "binary point" instead of a decimal point, what will the following numbers equal? That is, what are the base ten equivalents of the following binary numbers?

   • 0.101
   • 1.0111

   When you multiply a decimal number by 10, you shift the decimal point to the right one place. How can you shift a binary point to the right?

3. Rewrite the following base-ten numbers as 16-bit two's complement integers: -2, 31, and -50.

4. Write the number -8.625 in 32-bit floating point form.

5. Who proposed that the Klingon alphabet be added to Unicode? What is the status of the proposal? What are the Cirth and Tengwar alphabets, and what is the status of the corresponding proposals?

6. List three languages that you have never heard of whose alphabets are included in Unicode. Where are these languages spoken?

7. Consider the thirty-two bit pattern:

   0010 0110 0110 0111 0111 0100 0011 1011

   What is the interpretation of these thirty-two bits if you consider them to represent:

   • Four ASCII characters?
   • Two Unicode characters? (Feel free to draw these by hand.)
   • One 32-bit two's complement integer? (The standard Windows calculator might be handy here--put it into "Scientific" view.)
   • Extra credit for the masochistic: One floating-point number?

   You may find it helpful to turn the binary number into hexadecimal before searching the Unicode site.