Computer Organization and Structure
1. Convert 4096ten, -2,047ten, and -2,000,000ten 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 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 “new $s0 $s1”
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. Let’s try a set on less than operation using the values -7ten and 6ten. To make it simpler to follow the example, let’s 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 b’.
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 two’s complement integer?
b. an unsigned integer?
c. a single precision floating-point number?
d. a MIPS instruction?