Exam 2015

Question 1

Couple the law with its core element:
(A) Moore’s Law (1) Costs
(B) Rock’s Law (2) Energy
(C) Koomey’s Law (3) Boolean algebra
(D) DeMorgan’s Law (4) Transistors

a. (A)-(4); (B)-(2); (C)-(3); (D)-(1).
b. (A)-(4); (B)-(2); (C)-(1); (D)-(3).
c. (A)-(1); (B)-(4); (C)-(2); (D)-(3).
d. (A)-(4); (B)-(1); (C)-(2); (D)-(3).

Answer 1

d -> (A) Moore’s Law → (4) Transistors

(B) Rock’s Law → (1) Costs

(C) Koomey’s Law → (2) Energy

(D) DeMorgan’s Law → (3) Boolean Algebra

Question 2

“Cn XOR Cn-1”” does not indicate overflow for 2’s

Complement integer addition.

Answer 2

false, $C_n XOR C_{n-1}$ does indicate overflow for 2s complement integer addition

Question 3

Consider the multiplication of the following two numbers represented in 8-bit
2’s Complement:
0111 0011
0000 1111

What is the minimal number of addition/subtraction operations to perform this
multiplication?

Answer 3

4 operations have to be performed since 0000 1111 has 4 one-bit values (?)

Question 4

A two-digit octal number is erroneously interpreted as a decimal number, and thus its value larger by 4 (decimal) units. How much larger would the value have been if the number would have been erroneously interpreted as a hexadecimal number?

a. 16
b. 24
c. 32
d. 48

Answer 4

Let x be the first digit and y be the second digit.

• In octal base, the number xy is 8x + 1y
• In decimal, the number xy is 10x + 1y
• In hexadecimal, the number xy is 16x + 1y

We know the difference between the number xy between octal and decimal is 4: (10x + 1y) - (8x + 1y) = 4. Therefore, x = 2.

Now we have to find the difference between octal and hexadecimal: (16x + 1y) - (8x + 1y) = 8x. Since we found that x = 2, we can conclude that the hexadecimal number is 16 units larger.

Question 5

A measurement system records integer numbers that oscillate frequently. For example,
a sequence of measurements could result in +10, -10, +10, -10, etc. Which integer
representation should the system use?
a. Sign-and-Magnitude
b. One’s Complement
c. Two’s Complement
d. Excess-128

Answer 5

a -> Sign-and-Magnitude only requires changing the MSB to accommodate for the fluctuations between +10 and -10

Question 6

S = 0 11111111 00000000000000000000000

is a number in IEEE754 floating point representation.

What is the value of S?

a. -∞
b. +∞
c. +0
d. NaN

Answer 6

+∞