Practice Homework 2

1. Convert the following numbers from the bases as indicated.

   a.      1A7   (hex)                ______________________  (binary) 
   
   b.      372   (octal)              ______________________ (binary)
   
   c.      110111010101 (binary)      ______________________ (octal) 
   
   d.      10010101011  (binary)      ______________________ (hex) 
   
   e.      372   (octal)              ______________________ (hex) 
   
   f.      1A7   (hex)                ______________________ (octal) 
   
   

2. What is the biggest numeric value you can write in 8 bits using two's complement notation? Express it in both binary two's complement form and in decimal:

   two's comp  __________________________  decimal  ________________________
   
   

3. What is the smallest numeric value you can write in 8 bits using two's complement notation? Express it in both binary two's complement form and in decimal:

   two's comp  __________________________  decimal  ________________________
   
   

4. Convert the following decimal values to binary two's complement notation in 8 bits:

   a.	84		______________________
   
   b.	-84		______________________
   
   c.	15		______________________
   
   d.	-15		______________________
   
   e.	0		______________________
   
   f.	-128		______________________
   
   

5. Is it possible to express +128 in 8 bits using two's complement notation? If so, then write it below.

   ________________________
   
   

6. Is it possible to express +128 in 8 bits if we use unsigned numbers? If so, then write it below.

   ________________________
   
   

7. What is the biggest value we can express in 8 bits if we use unsigned numbers? Express it in both binary and in decimal:

   binary  __________________________  decimal  ________________________
   
   

8. What is the smallest value we can express in 8 bits if we use unsigned numbers? Express it in both binary and in decimal:

   binary  __________________________  decimal  ________________________
   
   

9. What are the decimal values of the following numbers, given that they are written using two's complement notation?

   a.	01100111		______________________
   
   b.	10011110		______________________
   
   c.	10000000		______________________
   
   d.	11111111		______________________
   
   e.	11111110		______________________
   
   

10. How can you distinguish a positive number from a negative number without doing any calculations if you see them expressed in 8-bit two's complement notation?
11. Suppose we use a machine that represents integers in 4 bits using two's complement notation.

    a.	Our integers act like what set of modulo numbers?  _________________
    
    b.	How many integers can be represented in the machine? _______________
    
    c.	What is the largest possible positive integer?  Express it in both binary and decimal.
    
    	binary:  _______________________  decimal:  ______________________
    
    d.	What is the smallest possible negative integer?  Express it in both binary and decimal.
    
    	binary:  _______________________  decimal:  ______________________
    
    

12. What is the smallest number of bits that can be used to store an integer on a computer which must be able to handle integers ranging from 1,000,000 down to -1,000,000?

    _______________________