**Homework Assignment 1 **

Due Sep. 2, 2009

- Problem 1.1. Instead of Base 13, represent the numbers from 8 to 23 in base 12.
- What is the exact number of bytes of a system that contains (1) 64K bytes, (b) 32 M bytes, (c) 7.6 G bytes?
- What is the largest binary number which can be expressed with 13 bits? What are the equivalent decimal and hexadecimal numbers?
- Convert the hexadecimal number 7C2A tobinary, and then convert it to octal.
- Convert the decimal number 576 to binary in two ways: (a) Convert directly to binary; (b) convert first to hexadecimal, then convert to binary.
- Express the following numbers in decimal:
(a) (10110.0101)

_{2}(b) (16.5)

_{16}(c) (26.24)

_{8}(d) (CDCD)

_{16} - Convert the following binary numbers to hexadecimal and decimal: (a)
1.001010
_{2}, (b) 100.1010_{2}. Explain why the decimal answer in (b) is 4 times that of (a). - 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

- (a) Find the 16's complement of C5A7
_{16}.(b) Convert C5A7

_{16}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)

- Do the following additions, where the numbers are 8 bits long:
- 53 + 7F
- 43 + A6
- C7 + 5A