CS 367 Section 002 Spring 2010
HW #3
Due Thursday, February 25 at classtime

1. (30 pts) Converting between representations
   Fill in the table below. If it is not possible to represent a value, explain why. Binary numbers are limited to 8 bits. Use twos complement for signed numbers.

   Decimal	Unsigned Binary	Signed Binary
   125
   -125
   219
   -219
   	01100101	-----
   	11010011	-----
   	-----	01010011
   	-----	10110111

2. (20 pts) Integer Addition
   Considering both signed (twos complement) and unsigned arithmetic, what is the result of adding each pair of 8 bit binary numbers. Characterize each result as:
   • Correct for both signed and unsigned representations
   • Correct for signed and incorrect for unsigned representations
   • Correct for unsigned and incorrect for signed representations
   • Incorrect for both signed and unsigned representations
   1. 01001000 + 00101100
   2. 01110000 + 01101100
   3. 11011001 + 01100011
   4. 11011001 + 11100011
   5. 00000000 + 11111111

3. (50 pts) Floating Point
   Assume a 10 bit floating point representation which uses the first bit as a sign bit, the next 5 for the exponent and the last 4 for the fraction. The bias is 15. Fill in the table below.

   Bit representation	e	E	f	M	V
   0 01101 0001
   1 10011 1010
   0 00000 1010
   		0		19/16
   					48.0
   					5/32

   What is the bit sequence for 0?

   What is the bit sequence and value for the largest possible normalized value?

   What is the bit sequence and value for the smallest possible positive normalized value?

   What is the bit sequence and value for the largest possible de-normalized value?

   What is the bit sequence and value for the smallest possible positive de-normalized value?