1. Given n bits, how many unsigned integers can be represented with the n bits? What is the range of these integers? (6 points)

2. There are 26 characters in the alphabet we use for writing English. What is the least number of bits needed to give each character a unique bit pattern? How many bits would we need to distinguish between upper- and lowercase versions of all 26 characters? (12 points)

3. Please answer the following: (12 points)
   1. What is the largest positive number one can represent in an 8-bit 2's complement code? Write your result in binary and decimal.

2. What is the greatest magnitude negative number one can represent in an 8-bit 2's complement code? Write your result in binary anddecimal.

3. What is the largest positive number one can represent in n-bit 2's complement code?
4. What is the greatest magnitude negative number one can represent in n-bit 2's complement code?

4. Convert the following 2's complement binary numbers to decimal. (9 points) a. 1010

b. 01011010

c. 11111110

5. Convert these decimal numbers to 8-bit 2's complement binary numbers. (18 points)

a. 102

b. -64

c. -33

6. Without changing their values, convert the following 2's complement binary numbers into 8-bit 2's complement numbers. (12 points)
   1. 1010

b. 011001

c. 1111111000

d. 01

7. Convert -31.25 to IEEE float in binary. (15 points)

8. Convert 0.1 to IEEE float in binary. Do not use any rounding and truncate the extra bits. (16 points)