Computer Organization and Structure

Homework #3

Due: 2005/11/22

1. Convert 512_ten, -1,023_ten, and -4,000,000_ten into 32-bit two’s complement binary numbers, respectively, and convert the following two’s complement binary numbers to be decimal numbers:

a. 1111 1111 1111 1111 1111 1110 0000 1100_two;

b. 1111 1111 1111 1111 1111 1111 1111 1111_two;

c. 0111 1111 1111 1111 1111 1111 1111 1111_two.

2. Find the shortest sequence of MIPS instructions to determine the absolute value of a two’s complement integer. Convert this instruction (accepted by the MIPS assembler):

abs $t2, $t3

This instruction means that register $t2 has a copy of register $t3 if register $t3 is positive, and the two’s complement of register $t3 if $t3 is negative. (Hint: It can be done with three instructions.)

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

1001_two – 0110_two = 1001_two + 1010_two = 0011_two

This result would suggest that -7_ten > 6_ten, 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 b’.

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

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

5. Show the IEEE 754 binary representation for the floating-point number 10_ten, 10.5_ten, 0.1_ten, and -2/3, respectively.