Computer Organization and Structure

 

Homework #3

Due: 2006/11/14

 

1.      Convert 4096ten, -2,047ten, and -2,000,000ten into 32-bit twofs complement binary numbers, respectively, and convert the following twofs complement binary numbers to be decimal numbers:

 

a.         1111 1111 1111 1111 1111 1111 0000 0110two;

b.        1111 1111 1111 1111 1111 1111 1110 1111two;

c.         0111 1111 1111 1111 1111 1111 1110 1111two.

 

2.      The following MIPS instruction sequence could be used to implement a new instruction that has two register operands. Give the instruction a name and describe what it does. Note that register $t0 is being used as a temporary.

 

srl     $s1, $s1, 1           #

sll     $t0, $s0, 31          # These 4 instructions accomplish gnew $s0 $s1h

srl     $s0, $s0, 1           #

or     $s1, $s1, $t0        #

 

3.      The ALU supported set on less than (slt) using just the sign bit of the adder. Letfs try a set on less than operation using the values -7ten and 6ten. To make it simpler to follow the example, letfs limit the binary representations to 4 bits: 1001two and 0110two.

 

1001two – 0110two = 1001two + 1010two = 0011two

 

This result would suggest that -7ten > 6ten, which is clearly wrong. Hence we must factor in overflow in the decision. Modify the 1-bit ALU in the following figures to handle slt correctly.

 

Figure 1: A 1-bit ALU that performs AND, OR, and addition on a and b or bf.

 

Figure 2: A 1-bit ALU for the most significant bit.

 

4.      Add 2.85ten x 103 to 9.84ten x 104 and add 3.63ten x 104 to 6.87ten x 103, respectively, assuming that you have only three significant digits, first with guard and round digits and then without them.

 

5.      Given the bit pattern:

 

1010 1101 0001 0000 0000 0000 0000 0010

 

what does it represent, assuming that it is

 

a.         a twofs complement integer?

b.        an unsigned integer?

c.         a single precision floating-point number?

d.        a MIPS instruction?