Academic Integrity: tutoring, explanations, and feedback — we don’t complete graded work or submit on a student’s behalf.

1. Which of the following number will represent a number X, where -8 ? X ? 7, in

ID: 3906314 • Letter: 1

Question

1. Which of the following number will represent a number X, where -8 ? X ? 7, in four bit 2’s compliment representation (hint: check -1 and 1)?

a. (X ? 0) ? X : (16 - X)

b. (X + 16) mod 16

c. (X ? 0) ? X : (invert X in binary format + 1)

d. all

2. When adding two n-bit 2’s complement numbers, overflow will not occur, if

a. Both operands have different sign bits

b. Both operands have same sign bits, and the sign bit of the result is also same

c. Carry-in bits to MSBs are same as the Carry-out bit from the MSB

d. All of the above

3.

[3 points] Calculate the average MIPS ratings for both machines. Which machine is faster (based on MIPS)?

Note that, 1 GHz = 10 9 Hz, and 1 million is 10 6

Instruction Class

Machine M1 – ML1

Machine M2 – ML2

Cycles/Instr Class

Frequency (%)

Cycles/Instr Class

Frequency (%)

LW

5

10

4

20

SW

4

20

4

10

Branch

3

10

3

20

Other I-type

1

20

2

10

R-type

1

30

1

30

J- type

1

10

1

10

BONUS-2 [3 points]: Which machine, M1 or M2, will spent more time on executing memory reference instructions? By how much (in nano seconds)?

4. [3 points] Decode the following 8-bit IEEE representation into their decimal value:
               (1) 1 011 1000                                                                           (2) 0 100 0000

Instruction Class

Machine M1 – ML1

Machine M2 – ML2

Cycles/Instr Class

Frequency (%)

Cycles/Instr Class

Frequency (%)

LW

5

10

4

20

SW

4

20

4

10

Branch

3

10

3

20

Other I-type

1

20

2

10

R-type

1

30

1

30

J- type

1

10

1

10

Explanation / Answer

2. When adding two n-bit 2’s complement numbers, overflow will not occur, if

a. Both operands have different sign bits

b. Both operands have same sign bits, and the sign bit of the result is also same

c. Carry-in bits to MSBs are same as the Carry-out bit from the MSB

d. All of the above

Answer) d. All of the above

As both the operands have different sign bits thus overflow does not occur and also if Both operands have same sign bits, and the sign bit of the result is also same overflow does not occur. Carry-in bits to MSBs are same as the Carry-out bit from the MSB.

4. [3 points] Decode the following 8-bit IEEE representation into their decimal value:

(1)10111000                                                   (2)01000000

Answer)

(1)10111000 - 184

(2)01000000 - 64