1. What is the range of numbers represented by 4 bytes when used to represent (a) unsigned integers, and (b) 2's complement signed integers?

2. (a) What is the maximum number represented by an 8-bit unsigned integer? What is the next value when this number is incremented by 1?

(b) What is the maximum number represented by an 8-bit, 2's complement binary integer? What is the next value when this number is incremented by 1?

3. (a) What is the maximum number represented by a 16-bit unsigned integer? What is the next value when this number is incremented by 1?

(b) What is the maximum number represented by a 16-bit, 2's complement binary integer? What is the next value when this number is incremented by 1?

4. What is the range of numbers represented by the IEEE floating-point notation for short real numbers (4 bytes) ?

5. How is the value 2 represented in the IEEE floating-point notation for short real numbers?

6. How is the value 1 represented in the IEEE floating-point notation for short real numbers?

7. How is the value 0 represented in the IEEE floating-point notation for short real numbers?

8. Write down the binary representation of the decimal value 2.625.

9. (a) Treat your seven-digit student number as one decimal number and convert it into its hexadecimal, octal and binary equivalent.

(b) Convert the binary result to its octal, hexadecimal and decimal equivalents in order to check your work from (a).

10. (a) Form the 2's complement of the binary number from 9(a) and convert it to its hexadecimal equivalent.

(b) Add this to the hexadecimal number from 9(a). Explain your result.

11. Take the seven digits of your student number and remove the most significant digit. Split the remaining number into two 3-digit numbers. Treating both numbers as decimal, convert the two into their binary equivalents and perform the following operations by hand. Show the result of each operation in binary, octal, hexadecimal, and decimal.

a) Form the AND of the two words

b) Form the OR

c) Form the XOR

d) Find the sum, treating the two words as unsigned numbers.

12. Using the two numbers as in Problem 11 above,

a) find the product of the two using an algorithm for binary multiplication,

b) divide the larger of the two by the smaller using an algorithm for binary division.

13. Devise a computer algorithm for performing a division operation.