ENEE 244 (01**). Spring 2006 

Homework 1

Due back in class on Friday, Feb 10.
 

1.  Convert the following binary numbers to decimal: (a) 1101; (b) 10111001.

2.  Convert the following decimal numbers to binary: (a) 23; (b) 498.

3. Convert the following numbers to decimal: (a) (34)₇; (b) (76)₈.

4. Convert (a) (47)₁₀ to radix 8; (b) (63)₁₀ to base 16.

5. Convert (a) (11010110111)₂ to hexadecimal; (b) (4532)₈ to binary.

6. Convert the following decimal numbers to binary: (a) 0.75; (b) 5.3.

7. Add the binary numbers (a) 0101 and 1001; (b) 01101.01 and 1001011.101.

8. Do the following subtractions: (a) 1100 - 1001; (b) 101101 - 11010.  

9. Multiply: 10100×101.

10.  Find the diminished radix complement of (a) (76)₈; (b) (10010)₂.

11.  Find the radix complement of (445)₁₀.

12.  Represent the following binary numbers in an 8-bit signed-magnitude scheme: (a) +1001; (b) -1011.

13.  A 6-bit computer uses the signed 2's complement representation.  It adds 10011 + 11101.  State the answer.  How is the overflow detected?  /* Hint: In such a representation, negative numbers are stored as 2's complement of their absolute value. Positive numbers are represented just like in the sign-magnitude scheme. */

14.  An 8-bit computer uses the signed 2's complement representation.  Show how this computer performs (a) 111010 - 1100; (b) 101 - 10110.  

15.  A 7-bit computer uses the signed 2's complement representation. What is the range of integers that can be represented in this scheme?