Homework Assignment 1
Due Sep. 3, 2010

1. (a) List the octal and hexadecimal numbers from 16 to 32.

   (b) Using A, B, C and D for the last four digits, list the numbers from 8 to 30 in base 14.

2. What is the exact number of bytes of a system that contains (1) 16K bytes, (b) 24 M bytes, (c) 12.5 G bytes?

3. What is the largest binary number which can be expressed with 14 bits? What are the equivalent decimal and hexadecimal numbers?

4. Convert the hexadecimal number 5A9C to binary, and then convert it to octal.

5. Convert the decimal number 391 to binary in two ways: (a) Convert directly to binary; (b) convert first to hexadecimal, then convert to binary.

6. Express the following numbers in decimal:

   (a) (11001.1011)₂

   (b) (A3.C)₁₆

   (c) (75.16)₈

   (d) (ABCD)₁₆

7. Convert the following binary numbers to hexadecimal and decimal: (a) 1.110101₂, (b) 1110.101₂. Explain why the decimal answer in (b) is 8 times that of (a).

8. Obtain the 1's and 2's complements of the following binary numbers:

   (a) 10000000

   (b) 00000000

   (c) 10011011

   (d) 01110110

   (e) 00110011

   (f) 11111111

9. (a) Find the 16's complement of A7C5₁₆.

   (b) Convert A7C5₁₆ to binary

   (c) Find the 2's complment of the result in (b).

   (d) Convert the answer in (c) to hexadecimal and compare it with the answer in (a)

10. Do the following additions, where the numbers are 8 bits long:

    1. 5F + 73

    2. A3 + 46

    3. A7 + 7A

11. Do the following subtractions, where the numbers are 8 bits long:

    1. 5F - 73

    2. A3 - 46

    3. A7 - 7A