Exam 2016 Flashcards
Link the concept with its computer generation:
(1) First Generation (A) Assembly
(2) Second Generation (B) Microprogramming
(3) Third Generation (C) Grid computing
(4) Fourth Generation (D) Transistor
(1) First Generation → (A) Assembly
(2) Second Generation → (D) Transistor
(3) Third Generation → (B) Microprogramming
(4) Fourth Generation → (C) Grid computing
Select which formula is not equivalent to the other given formulas.
a. !(!𝑥𝑦 ∙ !𝑦𝑧) + 𝑧𝑤
b. !(!(!(!𝑥𝑦 ∙ !𝑦𝑧)) ∙!𝑧𝑤)
c. !(!𝑥𝑦 + !𝑦𝑧 + !𝑧𝑤)
d. 𝑦(𝑥 + 𝑧) + !(!𝑧 + !𝑤)
C
a) can be transformed by de morgan to xy+yz+zw
b) has two negations that cancel out, making it !(!xy . !yz . !zw), which can then be changed to xy+yz+zw by de morgan
c) applying de morgan gives us xy . yz . zw which is already different from the first two
d) y(x+z) is the same as yx+yz and the second part can be changed to zw, so it is yx+yz+zw which is the same but in different order
This digital circuit realizes one of the following functions.
x1—–oD—->
Which?
a. OR
b. XOR
c. NAND
d. XOR
XOR
Truth table: 0110
Consider a CPU that has a single ALU that can only XOR two operands.
If you may only perform two operations on any number, which number representation
can be inverted by this ALU?
a. Numbers in 1C.
b. Numbers in 1C and 2C.
c. Numbers in 1C and SM.
d. Numbers in 1C, 2C, and SM.
c
SM: to invert the number, you only need to flip the first bit (the sign bit). To do this, you can xor the number with 1000, so this only requires one XOR gate
1C: to invert the number, you have to flip all the bits. To do this, you can xor the number with 1111 to invert it, so this only requires one XOR gate
What is the result of the following calculation?
NB: the subscripts indicate the radix and the binary number is in 2’s complement.
42(16) + 21(8) + 42(42) – 01010101(2)
a. 42
b. 82
c. 168
d. 338
c.
0100 0010 + 00010001 + 01010101 = 66 + 17 + 85 = 168
A two-digit octal number is erroneously interpreted as a decimal number, and thus its value is increased by 2 (decimal) units. How much larger would the value have been if the number would have been erroneously interpreted as a number using radix 42?
a. 1
b. 34
c. 42
d. 142
b
(42x + 1y) - (8x + 1y) = 34x
A measurement system records integer numbers that are uniformly random in nature.
For example, a long sequence of measurements with values between -2 and +2 could result in +1, -1, 0, -2, +2, etc., where each value appears with the same frequency.
Out of the following choices, which representation is the most efficient to use?
a. Sign-and-Magnitude
b. One’s Complement
c. Two’s Complement
d. IEEE 754
c -> 2’s complement has all combinations unique, therefore we can capture most numbers, therefore is probably the most suitable to use.
The following IEEE754 number is divided by 32768. What is the correct outcome?
1 10011111 00001101000011110000000
a. 1 10011111 00000000000000000001101
b. 1 10010100 11010000111100000000000
c. 1 10010000 11010000111100000000000
d. 1 10010000 00001101000011110000000
d -> 32768 is 2^15 thus only decrease exponent by 15
10011111 -> 10010000
Which of the following statements are correct?
I. Processors with hardwired control are easier to extend with complex
instructions than processors with micro-programmed control.
II. Micro-programmed control mechanisms are often implemented using a
Programmable Logic Array (PLA).
n/a
Given the function
𝑆 = (𝑥 + 𝑧)(𝑦 + 𝑤)(𝑤 + 𝑦)
How many zeroes appear in the truth table?
a. 0-2
b. 3-5
c. 6-8
d. 9-16
d -> truth table or karnaugh map
𝑆 = (𝑥 + 𝑧)(𝑦 + 𝑤)(𝑤 + 𝑦)
This formula is realized by one of the following digital circuits. Which?
b ->
1) Involution
$$
S = \overline{\overline{(x+z)(\overline{y}+\overline{w})(\overline{w}+y)}}
$$
2) DeMorgan
$$
S = \overline{\overline{(x+z)}+\overline{(\overline{y}+\overline{w})}+\overline{(\overline{w}+y)}}
$$
3) DeMorgan
$$
S = \overline{(\overline{x}·\overline{z})+(\overline{\overline{y}}·\overline{\overline{w}})+(\overline{\overline{w}}·\overline{y})}
$$
4) Involution
$$
S = \overline{(\overline{x}·\overline{z})+(y·w)+(w·\overline{y})}
$$
5) DeMorgan
$$
S = \overline{(\overline{x}·\overline{z})}·\overline{(y·w)}·\overline{(w·\overline{y})}
$$
6) Identity
$$
S = \overline{(\overline{x·x}·\overline{z·z})}·\overline{(y·w)}·\overline{(w·\overline{y·y})}
$$
We now know:
[(x nand x) nand (z nand z)] nand [y nand w] nand [w nand (y nand y)]
Couple the law with its related element:
(A) Moore’s Law (1) SIMD
(B) Rock’s Law (2) Cycles/Watt
(C) Koomey’s Law (3) 2’s Complement
(D) DeMorgan’s Law (4) Productie kosten/production costs.
a. (A)-(1); (B)-(2); (C)-(3); (D)-(4).
b. (A)-(1); (B)-(2); (C)-(4); (D)-(3).
c. (A)-(4); (B)-(1); (C)-(2); (D)-(3).
d. (A)-(1); (B)-(4); (C)-(2); (D)-(3).
d -> Moore’s Law → SIMD
- Moore’s Law: # of transistors in a microchip doubles every 2 years
- SIMD is short for “Single Instruction/Multiple Data” and refers to a computing method that enables processing of multiple data with a single instruction
Rock’s Law → Production costs
- Rock’s Law: the cost of semiconductor chip fabrication plant doubles every 2 years
Koomey’s Law → Cycles/Watt
- Koomey’s Law: # of computations per joule doubles every 1.5 years
DeMorgan’s Law → 2’s Complement
- DeMorgan’s Law: law in Boolean Algebra
- 2’s complement is a representation of integers
Which of the following statements are true?
- 0000 1000 00002 = 2008 = 12810 = 8016
- 0000 1010 00102 = 2428 = 16210 = B216
- 0001 0001 00002 = 04208 = 27210 = 11116
- 0011 1111 10002 = 17708 = 101610 = 3F816
- 0100 0000 00002 = 20018 = 102410 = 40016
- 1000 0000 00012 = 40008 = 204810 = 80016
(ATTN: The notation 1238 means: the value 123 in octal representation.)
a. 1, 2, 3, 4
b. 1, 2, 4, 5
c. 1, 4, 5, 6
d. Geen van de bovenstaande./ None of the above
d
Which of the following logic expressions indicate overflow for 2's Complement integer addition? a. Cn OR Cn-1 b. Cn OR Sn-1 c. Cn XOR Cn-1 d. Cn XOR Sn-1
c -> Explained in Hambacher 9.1.1
- C represents the carry-out bits in binary addition - If Cn and Cn-1 are different, there is overflow
Which of the following integer additions of 4-bit 2’s Complement leads to overflow?
(1) 0010 + 0011
(2) 0011 + 0100
(3) 0100 + 0111
(4) 1100 + 1001
(5) 0000 + 1000
a. 1 & 2
b. 3 & 4
c. 1 & 3 & 5
d. Geen van de bovenstaande./ None of the above
b -> Range of 2s complement: $[-2^{n-1}, 2^{n-1}-1]$
Therefore, the range for 4-bit addition = $[-8, 7]$
Overflow occurs when the sum of the addition is out of range
*Note: remember to find the 2s complement of these numbers first before evaluating
