CS350 Intro Computer Systems Homework 3

Homework 3 Integer and Floating Point Arithmetic

1. For signed and unsigned multiplication, fill in the following table showing the results of multiplying different 5-bit numbers, in the style of Figure 2.27 of textbook (page 98) for w=5, by replacing "decimal" with decimal values and "binary" with binary values.

   	Mode	x		y		x*y, w=10		Truncated x*y, w=5
   (a)	Unsigned	decimal	10000	decimal	10101	decimal	binary	decimal	binary
   	Two's complement	decimal	10000	decimal	10101	decimal	binary	decimal	binary
   (b)	Unsigned	decimal	10101	decimal	01000	decimal	binary	decimal	binary
   	Two's complement	decimal	10101	decimal	01000	decimal	binary	decimal	binary
   (c)	Unsigned	decimal	01100	decimal	11001	decimal	binary	decimal	binary
   	Two's complement	decimal	01100	decimal	11001	decimal	binary	decimal	binary
   (d)	Unsigned	decimal	01010	decimal	00101	decimal	binary	decimal	binary
   	Two's complement	decimal	01010	decimal	00101	decimal	binary	decimal	binary

2. Do problem 2.77.
3. Write a C program to print the binary values of a floating point number passed as a parameter, as demonstrated in class, by filling in ftob.c. For example, it would print "0 01111110 10000000000000000000000" when you type "ftob 0.75." So would it "0 01111101 00110011001100110011010" when you type "ftob 0.3" as demonstrated in class.
4. Round the following fractional values to the nearest quarter (2 bits to the right of the binary point), according to the round-to-even rule in the style of page 26 of Lecture note 4 (04-float.pdf).

   Value	Binary	Rounded	Action	Rounded Value
   1 1/16
   1 3/16
   2 5/16
   2 5/8
   3 5/8
   3 7/8

5. Convert the following decimal values to 9-bit floats, where bit 8 (the most signifincant bit) is the sign bit, bits 4-7 are exponents, and the rest (bits 0-3) are the significand. Follow the format of page 39 of Lecture note 4 (04-float.pdf).

   Value	Rounded	Exp	Adjusted	Result
   256
   31
   33
   35
   276
   127

6. Write a C program to print the decimal value of a binary string passed as a parameter. For example, it would print 0.75 when you type "0 01111110 10000000000000000000000."
   As another example, it would print 0.125 when you type "0 01111100 00000000000000000000000."