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	01111101	01111101
   -125	smaller than UMIN	10000011
   219	11011011	greater then TMAX
   -219	smaller than UMIN	smaller than TMIN
   101	01100101	-----
   211	11010011	-----
   83	-----	01010011
   -73	-----	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 = 01110100 - correct for both
   2. 01110000 + 01101100 = 11011100 - correct for unsigned only
   3. 11011001 + 01100011 = 00111100 - correct for signed only
   4. 11011001 + 11100011 = 10111100 - correct for signed only
   5. 00000000 + 11111111 = 11111111 - correct for both

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	13	-2	1/16	17/16	17/16 * 1/4 = 17/64
   1 10011 1010	19	4	10/16	26/16	-26/16 * 16 = -26.0
   0 00000 1010 denormalized	0	-14	10/16	10/16	10/16 * 1/(2**14)
   0 01111 0011	15	0	3/16	19/16	19/16
   0 10100 1000	20	5	8/16	24/16	48.0
   0 01100 0100	12	-3	4/16	20/16	5/32

   What is the bit sequence for 0?
   0 00000 0000

   What is the bit sequence and value for the largest possible normalized value?
   0 11110 1111 which is 31/16 * (2**15)

   What is the bit sequence and value for the smallest possible positive normalized value?
   0 00001 0000 which is 1/(2**14)

   What is the bit sequence and value for the largest possible de-normalized value?
   0 0000 1111 which is 15/16 * 1/(2**14)

   What is the bit sequence and value for the smallest possible positive de-normalized value?
   0 0000 0001 which is 1/16 * 1/(2**14)