Homework Assignment 1
Due Sep. 2, 2009

1. Problem 1.1. Instead of Base 13, represent the numbers from 8 to 23 in base 12.

2. What is the exact number of bytes of a system that contains (1) 64K bytes, (b) 32 M bytes, (c) 7.6 G bytes?

3. What is the largest binary number which can be expressed with 13 bits? What are the equivalent decimal and hexadecimal numbers?

4. Convert the hexadecimal number 7C2A tobinary, and then convert it to octal.

5. Convert the decimal number 576 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) (10110.0101)₂

   (b) (16.5)₁₆

   (c) (26.24)₈

   (d) (CDCD)₁₆

7. Convert the following binary numbers to hexadecimal and decimal: (a) 1.001010₂, (b) 100.1010₂. Explain why the decimal answer in (b) is 4 times that of (a).

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

   (a) 10000000

   (b) 00000000

   (c) 11010010

   (d) 01001010

   (e) 00110101

   (f) 11111111

9. (a) Find the 16's complement of C5A7₁₆.

   (b) Convert C5A7₁₆ 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. 53 + 7F

    2. 43 + A6

    3. C7 + 5A