The document provides examples and explanations of basic theory concepts in computer science and mathematics. It contains 16 multiple choice questions covering topics like: binary and hexadecimal number representations and arithmetic, Boolean logic, probability, standard deviation, combinatorics, and floating point number representation. The questions are at a basic to intermediate level and are intended to test understanding of fundamental concepts.

1. Basic Theory (FE)
by Tanat Tonguthaisri
itpe@nstda.or.th

2. 1. Which of the following arithmetic expressions is
correct? Here, a number is written in radix notation;
that is, a decimal subscript following the number (i.e.
numberradix) is used to indicate the radix.
a) 10102 + 108 = 1710
b) 11012 + 416 = 1710
c) 148 + 112 = 1610
d) B16 + 102 = 1410

3. 10102 + 108 = 1710
8+2 + 8 = 18
11012 + 416 = 1710
8+4+1 + 4 = 17
148 + 112 = 1610
8+4 + 2+1 = 15
B16 + 102 = 1410
11 + 2 = 13

4. 2. When the binary fraction 11101.110 is subtracted
from the binary fraction 101101.101, what is the correct
result?
a) 111.001
b) 111.111
c) 1111.001
d) 1111.111

5. 101101.101 – 11101.110
= 101101.101 – (11101.101 + 0.001)
= 101101.101 – 11101.101 - 0.001
101101.101
11101.101
10000.000
10000.000 – 0.001 = 1111.111

6. 3. When a certain natural number x can be
represented by a 2n-digit binary number consisting of 1
and 0 arranged alternately, i.e. 1010...10, which of the
following equations holds for x?
a) x + x /2 = 2 2 n
b) x + x /2= 2 2 n -1
c) x + x /2= 2 2 n +1
d) x + x /2= 2 2 n +1 -1

7. http://getphilnitscertified.wordpress.com/
2011/10/27/2007-october-fe-am-
q3/#more-474

8. 4. There is an 8-bit numerical value, where a negative
number is represented in two’s complement. When
this value is represented in decimal, it becomes -100.
When this value is regarded as an unsigned number,
which of the following is the correct value in decimal?
a) 28
b) 100
c) 156
d) 228

9. 8-bit  11111111 = 255
100 = 64 + 32 + 4
= 2 6 + 25 + 22
= 011001002
100110112 = 155
155 + 1 = 156

10. 5. When multiple values are added arithmetically, it is
recommended that the values be added sequentially,
starting from the number whose absolute value is the
smallest. Which of the following errors can be reduced
by means of this method?
a) Cancellation of significant digits
b) Loss of trailing digits
c) Truncation error
d) Underflow

11. 6. The figure below shows daily changes in the weather for a given
district, and each value represents the probability of changes in the
following day’s weather. When the weather is rainy on a given day, what
is the probability that the weather is clear two days later?
a) 0.15
b) 0.27
c) 0.3
d) 0.33

12. Rainy, Rainy, Clear = 0.2 x 0.3
Rainy, Clear, Clear = 0.3 x 0.4
Rainy, Cloudy, Clear = 0.5 x 0.3
0.3 x (0.2 + 0.4 + 0.5) = 0.3 x 1.1
= 0.33

13. 7. Which of the following
operations does not change the
lower 4 bits of an 8-bit string?
a) A logical product (i.e. AND) with a bit string 0F in
hexadecimal
b) A logical sum (i.e. OR) with a bit string 0F in
hexadecimal
c) A negative logical product (i.e. NAND) with a bit string
0F in hexadecimal
d) An exclusive logical sum (i.e. exclusive OR) with a bit
string 0F in hexadecimal

14. 8. In a certain company, there are a total of 400
employees including 100 smokers. The number
of male employees is 250, including 75 male
smokers. What is the probability that an
employee selected at random is a female
nonsmoker?
a) 3 b) 3 c) 5 d) 5
4 8 6 16

15. 100 smokers – 75 male smokers
= 25 female smokers
400 employess – 250 male employees
= 150 female employees
150 female employees – 25 female smokers
= 125 female non-smokers
125 / 400 = 5 / 16

16. 9. The decision table shown below is used to determine whether
or not an order can be accepted in a sales order processing
system. Which of the following logical expressions is equivalent
to “Accept order”? Here, “NOT” is used for the logical negation,
“AND” for the logical product, and “OR” for the logical sum.
Bad debt within 2 Years (X) Y Y Y Y N N N N
Credit excess $10,000 (Y) Y Y N N Y Y N N
Age of customer > 10 Years (Z) Y N Y N Y N Y N
Accept order X X X
Reject order X X X X X
a) (NOT X) AND (NOT Y OR NOT Z)
b) (NOT X) AND (NOT Y OR Z)
c) (NOT X) AND (Y OR Z)
d) X AND (NOT Y OR NOT Z)

17. Bad debt within 2 Years (X) Y Y Y Y N N N N
Credit excess $10,000 (Y) Y Y N N Y Y N N
Age of customer > 10 Years (Z) Y N Y N Y N Y N
Accept order X X X
Reject order X X X X X
(not X and Y and Z) or (not X and not Y)
= not X and [ (Y and Z) or not Y ]
= not X and (Z or not Y)

18. 10. Which of the following sets is equivalent to
the set S -(T  R)? Here, “  stands for a
”
product set operation, “  for a union set
”
operation, and “-” for a difference set operation.
a) (S –T )-R
b) (S –T )  (S –R )
c) (S –T )  (T –R )
d) (S –T )  (T –R )

19. 11. The figure below shows the state transition diagram
of an automaton that accepts bit strings with even
numbers of 1s. The double circle marked with “Even”
represents the accepted state. Which of the following
combinations should be inserted in the blank boxes
labeled A and B ?
A B
a) 0 0
b) 0 1
c) 1 0
d) 1 1

20. 12. Which of the following represents
the hexadecimal fraction 3A.5C as a
decimal fraction?
939 3735
a) b)
16 64
14939 14941
c) 256 d) 256

21. 0.5C16 = 5 x 16-1 + 12 x 16-2
= 16-1 x (5 + 12/16)
= 16-1 x (5 + ¾)
= 16-1 x 23/4
= 23 / 64
3A16 = 3 x 16 + 10 = 58
3A.5C16 = 58 + 23/64
= (58x64 + 23) / 64
= (3,712 + 23) / 64
= 3735/64

22. 13. Which of the following hexadecimal numbers,
representing signed 16-bit binary numbers, results in
overflow when multiplied by 4? Here, a negative
number is represented in 2’s complement.
a) 1FFF
b) DFFF
c) E000
d) FFFF

23. 1FFF
0 001 1111 … x 4 = 111 11 … 00
DFFF
1 101 1111 ...  010 0000 …
E000
1 110 0000 …  001 1111 …
FFFF
1 111 1111 …  000 0000 …

24. 14. Which of the following is the
appropriate reason why the mantissa
is normalized in the floating point
representation?
a) The arithmetic operation algorithm can be
simplified.
b) The maximum number of significant digits can be
maintained.
c) The range of representable values can be
expanded.
d) The relative size relationships can be investigated
as if in fixed point numbers.

25. 15. The function f(x) has a real-type argument and a
real-type return value. The procedure using this
function is shown in the steps 1 through 5. When
this procedure is executed repeatedly a sufficient
number of times and the value of y stops changing
in the step 3, which of the following expressions
holds?
[Steps] a) f(a) = y
1. x ← a
2. y ← f(x) b) f(y) = 0
3. Display the value of y
4. x ← y c) f(y) = a
5. Return to the step 2
d) f(y) = y

26. 16. The student scores in a certain examination are
shown in the table below. What is the standard
deviation of these student scores? Here, the
standard deviation δ can be defined as follows:
“δ” is a positive number, and “n” is the number of sample
values. “xi” is each sample value, and “ x” is an
arithmetic average of the sample values.
Student name Score
a) 10
Mr. Brown 30 b) 20
Ms. Rose 50
Mr. White 60 c) 30
70
Ms. Green
Mr. Black 90 d) 60

27. Mean = (30+50+60+70+90) / 5 = 60
(30-60)2 + (50-60)2 + (60-60)2 + (70-60)2 + (90-60)2
= 302 + 102 + 102 + 302
= (9 + 1 + 1 + 9) x 102
= 20 x 102
Variance = 20 x 102 / 5 = 4 x 102
Standard deviation = square root (400) = 20

28. 17. There are three different sizes of white balls and
three different sizes of green balls. When these six
balls are laid out in a line so that the three white balls
can be placed in adjacent positions, how many
arrangements of all the balls can be made?
a) 10
b) 144
c) 576
d) 720

29. No. of ways 3 different white balls can be
arranged = 3! = 6
No. of ways 3 different green balls plus white
group can be arranged = 4! = 24
Overall no. of ways = 6 x 24 = 144

30. 18. Which of the following expressions results in a loss
of trailing digits when calculated by a computer whose
floating-point representation has a 23-bit mantissa?
Here, the numbers in “( )2” are represented in binary.
a) (10.101)2×2–16–(1.001)2×2–15
b) (10.101)2×216–(1.001)2×216
c) (1.01)2×218+(1.01)2×2–5
d) (1.001)2×220+(1.1111)2×221

31. 19. There is a device consisting of Unit A, Unit B, and
Unit C. Each unit can execute the “exclusive OR”
operation in units of 4 bits. When an input bit string
1101 is given, an output bit string 0100 is obtained. In
this device, if the internal key for Unit B is changed and
the output bit string 1111 is generated, which of the
following is the newly changed internal key for Unit B?
a) 1011
b) 1100
c) 1101
d) 1110

32. 1101
0001 Key A
1100 1100
0101 Key B 1110
1001 0010
1101 Key C 1101
0100 Output 1111

33. 20. As shown in the truth table below, when an output
signal is generated using three input signals A, B, and
C, which of the following Boolean expressions can be
applied to the output signal? Here, “ ” stands for the
logical product, “ ” for the logical sum, and “ X for the
”
logical negation of “X”.
Input signal
a)
Output signal
A B C A BC
0 0 0 0
0
0
0
1
1
0
1
1 b) A  ( B  C)
c)
0 1 1 1
1 0 0 0 A BC
1 0 1 0
1
1
1
1
0
1
0
0
d) A  ( B  C)

34. Input signal
Output signal
A B C
0 0 0 0
0 0 1 1
0 1 0 1
0 1 1 1
1 0 0 0
1 0 1 0
1 1 0 0
1 1 1 0
A  ( B  C)

35. 21. A “negative AND” operation “X NANDY” of X and
Y is defined as “NOT (X AND Y)”. Which of the
following is the logical expression that represents “X
OR Y” by using NAND only?
a) ((X NAND Y) NAND X) NAND Y
b) (X NAND X) NAND (Y NAND Y)
c) (X NAND Y) NAND (X NAND Y)
d) X NAND (Y NAND (X NAND Y))

36. X OR Y = NOT (NOT X AND NOT Y)
= NOT X NAND NOT Y
= (X NAND X) NAND (Y NAND Y)
Input A Output Q
0 1
1 0

37. 22. Which of the following is included as an
element of a set of character strings represented
by a regular expression “[A–Z]+[0–9]*”? Here, the
regular expression follows the rules described
below.
[A – Z] denotes a single alphabetical letter.
[0 – 9] denotes a single numeral. a) 456789
The symbol “*” denotes zero or more
repetitions of the immediately preceding b) ABC99*
regular expression.
The symbol “+” denotes one or more c) ABC+9
repetitions of the immediately preceding
regular expression. 9
d) ABCDE

38. 23. When the equation “100n–34n=44n” holds, which of
the following represents 26n? Here, each number is
written in radix notation; that is, each subscript “n”
indicates the radix. In addition, when there is no
subscript, the radix 10 is implied.
a) 18
b) 20
c) 22
d) 38

39. 100n – 34n = 44n
1xn2 – (3xn + 4) = 4xn + 4
n2 -3n -4n -4 -4 = 0
n2 – 7n – 8 = 0
(n – 8)(n + 1) = 0
n = 8, -1
n=8
26n = 268 = 2x8 + 6 = 22

40. 24. In the truth table shown below, which of the
following is the correct combination of output values
x1, x2, and x3? Here, “·” stands for the logical product,
“+” for the logical sum, “ ” for the⊕exclusive OR, and
“ ” for the logical negation of “X”.
X
Input Output
AB C D ( A ⋅ B) + (C ⊕ D)
a) 0 0 1
010 1 x1
b) 1 0 0
111 0 x2 c) 1 0 1
110 0 x3 d) 1 1 0

41. 25. Which of the following expressions can be used
to calculate the quarter number (for example, “1” for
January through March) for the n-th month of the
year? Here, “n” ranges from “1” for January to “12”
for December, and each fractional part of the
resulting values is truncated.
n −1
a)
3
n −1
b) 3
+1
n
c)
3
n
d) 3
+1

42. 26. When the resulting value of the expression
“13× 3+11 162+9 
16 16+3” is represented in binary,
how many “1” bits are included in the binary value?
a) 6
b) 10
c) 13
d) 16

43. 13x163 + 11 = D00B16
162 + 9 = 010916
16 + 3 = 001316
D00B16 B = 10112
010916 9 = 10012
001316 3 = 00112
D11B16 1011
D = 11012

44. 27. When the simultaneous equations shown
below hold for the Boolean variables w, x, y,
and z, which of the following is the correct
solution? Here, “+” stands for the logical sum
operation, and “·” for the logical product
operation.
x·y = 0
w x y z
x·z + w = 1
x·y + w = 0
a) 0 0 1 0
b) 0 1 0 0
c) 0 1 0 1
d) 1 1 0 1

45. x·y = 0
x·z + w = 1
x·y + w = 0  w = 0
x·z + w = 1  x·z = 1
x=1,z=1
x·y = 0  1·y = 0
y=0

46. 28. There is an 8-bit register where integers are
represented in binary by using 2’s complement for
negative numbers. When the decimal integer “–24” is
stored in the register and then arithmetically shifted 2
bits right, what is the resulting value in decimal? Here,
the leftmost bit of the register is used as a sign bit.
a) -102
b) -96
c) -6
d) 5

47. 256-24 = 232
232 = 128 + 64 + 32 + 8
= 111010002
111101002
111110102
000001012 = 5  One’s complement
5 + 1 = 6  Two’s complement

48. 29. When a single-bit “half adder” circuit is used for simply
adding two input signals x1 and x2, which of the following is
the appropriate combination of logical expressions for two
output signals s (sum) and c (carry)? Here, “+” stands for
the logical OR operation and “ ” for the logical AND ⋅
operation.
s c
a) x1 + x2 x1 ⋅ x2
b) x1 ⋅ x2 x1 + x2
c) ( x1 + x2 ) ⋅ ( x1 ⋅ x2 ) x1 ⋅ x2
d) ( x1 + x2 ) + ( x1 ⋅ x2 ) x1 + x2

49. 30. Which of the following prefix expressions is
equivalent to the infix expression “(A+B)*C–(D–E)”?
a) –*+ABC–DE
b) –+AB*C–DE
c) AB+C*–DE–
d) AB+C*DE––

50. 31. The syntax rules of the field identifier “field ID” are
represented in BNF notation as shown below. When each ID
is defined as an arbitrary sequence of letters and/or digits,
which of the following should be inserted into the blank A?
<field ID> ::= <ID> | <field ID>.<ID>
<ID> ::= A
<letter> ::= a|b|с|d|e|f|g|h|i|j|k|l|m|n|o|p|q|r|s|t|u|v|w|x|y|z
<digit> ::= 0|1|2|3|4|5|6|7|8|9
a) <ID>.<letter>|<ID>.<digit>
b) <ID><letter>|<ID><digit>|<ID>.<ID>
c) <letter>|<digit>|<ID><letter>|<ID><digit>
d) <letter><ID>|<digit><ID>

51. 32. According to a survey of 100 students, there are 40 students
studying English, 30 studying French, and 25 studying Spanish.
In addition, 8 students are studying English and French, 6 are
studying English and Spanish, 5 are studying French and
Spanish, and 22 are not studying any of the three languages.
Which of the following is the number of students studying all
three languages?
a) 1
b) 2
c) 3
d) 4

52. (40 + 30+ 25) – (8 + 6 + 5) + x = 100 – 22
x = 78 – 95 + 19 = 2

53. 33. When three subsets A, B, and C exist in the universal set S
as shown in the diagram below, which of the following
represents the shaded area? Here, each of A, B, and C
indicates the area encompassed by the corresponding circle.
stands for the union set of X and Y, for the intersection set of X
and Y, for the relative complement set of Y in X, and for the
mutually exclusive set of X and Y.
a) ( A  B)  ( A  C )  (B  C )
b) (( A  B)  ( A  C)  (B  C))  ( A ⊕ B ⊕ C)
c) ( A  B  C ) − ( A ⊕ B ⊕ C )
d) ( A  B  C ) − ( A  B  C )

54. 34. When the true and measured values are 1.744 and 1.720
respectively, what is the approximate relative error in
percentage?
a) -2.4
b) -1.4
c) 1.4
d) 2.4

55. 1.744 – 1.720 = 0.024
0.024 / 1.744 x 100% = 1.4%

56. 35. What is the probability of getting a sum of 8 or 9
on a pair of dice, each of which is a regular
hexahedron with faces numbered 1 through 6?
1 5
a) b)
18 36
1 1
c) 4 d) 3

57. Sum is 8  6 2, 5 3, 4 4, 3 5, 2 6
Sum is 9  6 3, 5 4, 4 5, 3 6
5 + 4 = 9 combinations
9 / (6x6) = 9 / 36 = 1/4

58. 36. An adjacency matrix is used for representing which
vertices of a directed or undirected graph are adjacent to
which other vertices. Which of the following is the
appropriate matrix that can represent the directed graph
below?
a) b) c) d)
A B C A B C A B C A B C
A 1 1 1 A 1 0 1 A 0 1 1 A 0 1 0
B 1 1 1 B 0 1 0 B 1 0 1 B 1 0 1
C 0 0 1 C 1 1 1 C 0 0 1 C 0 0 0

59. (III) When the runtime complexity of an algorithm is represented
by n2, which of the following is the running time for the algorithm
to process one million elements? Here, n is the number of
elements to be processed by this algorithm, and it takes 1
nanosecond to process only one element.
a) 1 nanosecond
b) 1 millisecond
c) 1 second
d) 1,000 seconds

60. 37. Which of the following is equivalent to the result of the
arithmetic expression “ 7538 − A616 Here, each number is
”?
written in radix notation; that is, the radix is represented by a
subscript following the number.
a) 1010011012
b) 5018
c) 32510
d) 13516

61. (7 x 82 + 5 x 8 + 3) – (10 x 16 + 6)
= 8 x (7x8 + 5 – 10 x 2) – 3
= 8 x (56 + 5 – 20) – 3
= 8 x 41 – 3
= 328 – 3
= 325

62. 38. Which of the following is equivalent to the logical expression
“not ( A ≤ B or C < D Here, A, B, C, and D are variables, and
)”?
the resulting values of “ A ≤ B ” and “ C < Dcan be either 1 for
”
true or 0 for false.
a) A< B and C≤D
b) A> B and C≥ D
c) A< B and C≤D
d) A> B and C≥ D

63. 39. Which of the following is a logical equation
that is equivalent to the logic circuit shown below?
Here, the “•” is the logical product, “+” is the
logical sum, and is the negation of X.
a) Z = ( A + B) + (C ⋅ D)
b) Z = ( A + B) + (C ⋅ D)
c) Z = ( A ⋅ B) ⋅ (C + D)
d) Z = ( A ⋅ B) ⋅ (C + D)

64. 40. An empty tank can be filled with water in 20 minutes by
using Pipe A or in 30 minutes by Pipe B, and the tank filled with
water can be emptied of water in 40 minutes by using Pipe C.
When the three pipes A, B, and C work together, approximately
how long (in minutes) does it take to fill the empty tank with
water?
a) 9.2
b) 10.0
c) 17.1
d) 24.0

65. A: x/20 B: x/30 C: -x/40
x/20 + x/30 – x/40
= (6x + 4x – 3x)/120
= 7x/120
Fill x in 120/7 = 17.1 minutes

66. 41. Which of the following is the binary fraction that is equivalent
to the decimal fraction 115.625?
a) 1100111.1001110001
b) 1100111.101
c) 1110011.1001110001
d) 1110011.101

67. 115 = 64 + 32 + 16 + 2 + 1
= 2 6 + 25 + 24 + 2 1 + 2 0
= 11100112
0.625 x 2 = 1.25 ----- (0.1) 2
0.25 x 2 = 0.5 -------- (0.10) 2
0.5 x 2 = 1.0 ----------- (0.101) 2
1110011.1012

68. 42. Which of the following is equivalent to the logical expression
below? Here, “AND” has higher precedence than “OR”, and
“NOT” has the highest precedence.
x AND (y OR z) OR y AND (x OR z) OR x AND y AND z
a) x AND y OR x AND z OR y AND z
b) x AND y OR x AND z OR y AND z OR x AND (NOT
y)
c) x AND y OR z OR y AND x OR z OR x AND y AND
z
d) x AND z OR y AND z OR x AND y AND z

69. 43. How many multiplications at a minimum
must be performed in order to calculate the
polynomial expression “x4–2x3+5x2+x–6”?
a) 2
b) 3
c) 5
d) 6

70. 44. How many binary numbers can be
represented using a 6-bit number that does
not have two contiguous 1s? For example,
“101010” does not have two contiguous 1s.
a) 8
b) 13
c) 21
d) 34

71. 000000 101010 100001
100000 010101 101001
010000 100100 100101
001000 010010 101000
000100 001001 010100
000010 100010 001010
000001 010001 000101

72. 45. When the expression
(A – 2 x ( B + C) - D x E) x F
in conventional infix notation is converted to the
prefix expression, which of the following
represents the resulting expression?
a) A2 BC + × − DE × − F ×
b) A2 BC + × − DE × F − ×
c) × − − A × 2 × B + CDEF
d) × − − A × 2 + BC × DEF

73. 46. When the figure below shows the process flow of a
compiler that is used for procedural languages, which of
the following is the appropriate combination that should
be inserted into blanks A though C?
A B C
a) Lexical analysis Semantic analysis Syntax analysis
b) Lexical analysis Syntax analysis Semantic analysis
c) Semantic analysis Syntax analysis Lexical analysis
d) Syntax analysis Lexical analysis Semantic analysis