Data Representation MCQ Questions and Answers
1. Which of the following is NOT a primitive data type in most programming-language type systems?
A. Integer
B. Floating point
C. Record
D. Character
2. The base (radix) of the hexadecimal number system is:
A. 8
B. 10
C. 16
D. 2
3. What is the 2’s complement of the 8-bit binary number 00110110?
A. 11001010
B. 11001010
C. 11001001
D. 11001110
4. Which representation is typically used for real numbers in IEEE 754 single precision?
A. Sign-Magnitude only
B. Two’s complement integer with scale factor
C. Sign bit, biased exponent, and mantissa (fraction)
D. Excess-0 notation
5. When adding two unsigned binary numbers, an overflow occurs if:
A. The sign bit changes
B. A carry out of the most significant bit occurs
C. A carry out from the most significant bit occurs (for fixed-width representation)
D. Two’s complement is used
6. Which code is a weighted binary code commonly used in digital systems for decimal digit representation?
A. Excess-3
B. 8421 BCD
C. Gray code
D. Hamming code
7. Which of the following number systems uses negative weights for digits?
A. Binary
B. Decimal
C. Balanced ternary
D. Hexadecimal
8. Convert binary 1101.101₂ to decimal.
A. 13.625
B. 13.625
C. 11.625
D. 14.5
9. The main advantage of Gray code is:
A. Simpler arithmetic operations
B. Higher density storage
C. Only one bit changes between successive values
D. Lower power consumption always
10. Which error-detection code appends a parity bit to detect single-bit errors?
A. CRC
B. Parity check
C. Hamming code
D. BCH code
11. In signed magnitude representation, the most significant bit (MSB) denotes:
A. Magnitude bits
B. Sign
C. Exponent
D. Parity
12. Convert decimal -18 into 8-bit two’s complement binary.
A. 11101110
B. 11101110
C. 11101110
D. 11110010
13. The bias used in IEEE 754 single-precision exponent is:
A. 127
B. 127
C. 1023
D. 15
14. Which complement gives the value of a negative integer as (base^n − magnitude)?
A. 1’s complement
B. Sign-magnitude
C. 2’s complement
D. Excess-K
15. For fixed-point representation with Q-format Qm.n, the ‘n’ indicates:
A. Integer bits
B. Fractional bits
C. Total bits
D. Exponent bits
16. In floating-point arithmetic, catastrophic cancellation refers to:
A. Loss of exponent bits
B. Rounding up always
C. Significant relative error when subtracting nearly equal numbers
D. Overflow to infinity
17. What is the Hamming distance between binary words 1011101 and 1001001?
A. 2
B. 3
C. 3
D. 4
18. Which algorithm computes integer multiplication using shifts and adds and is efficient in hardware?
A. Booth’s algorithm
B. Shift-and-add (array multiplier) and Booth’s algorithm
C. Newton-Raphson
D. Karatsuba only
19. In unsigned binary division, if the divisor is greater than dividend, the quotient and remainder are:
A. Quotient = 0, remainder = 0
B. Quotient = 1, remainder = dividend
C. Quotient = 0, remainder = dividend
D. undefined
20. Which of the following is true for 1’s complement representation of negative numbers?
A. There is a unique zero
B. There are two zeros (+0 and −0)
C. Range is symmetric with two’s complement
D. Arithmetic is identical to two’s complement
21. What does the IEEE 754 representation value “exponent all ones and fraction zero” signify?
A. Normalized number
B. Denormalized number
C. Infinity (depending on sign bit)
D. Not a Number (NaN)
22. Convert hexadecimal 3A.F to binary.
A. 0011 1010 . 1111
B. 00111010.1111
C. 111010.1111
D. 001110101111
23. Which checksum method treats data as a sequence of words and adds them (modulo 2^n)?
A. CRC
B. Internet checksum (ones’ complement addition)
C. Parity bit
D. Hamming code
24. Which number system is most compact for representing large integers with few digits?
A. Binary
B. Decimal
C. Hexadecimal
D. Octal
25. What is the result of adding two IEEE 754 single-precision numbers when exponents differ greatly?
A. Exact sum always
B. Subnormal result only
C. Small number may be lost due to alignment and rounding
D. Exception thrown
26. Which of the following is NOT an error-detecting/detecting-and-correcting code?
A. Parity bit
B. CRC
C. Hamming code
D. Two’s complement
27. Convert decimal 0.3125 to binary fractional representation.
A. 0.0101
B. 0.0101₂
C. 0.0101₂
D. 0.0011
28. In fixed-point Q1.15 format (16-bit), what is the smallest positive representable increment?
A. 2^{-1}
B. 2^{-8}
C. 2^{-15}
D. 2^{-16}
29. The primary purpose of biasing the exponent in IEEE floating point is to:
A. Allow negative mantissas
B. Simplify sign handling
C. Represent both positive and negative exponents as unsigned values
D. Improve precision
30. Which arithmetic property fails for floating-point numbers due to rounding?
A. Commutativity of addition
B. Associativity of addition
C. Multiplication distributivity over addition
D. Associativity of addition and sometimes distributivity
31. What is the 1’s complement of 01011011?
A. 10100100
B. 10100100
C. 11001011
D. 10011011
32. Which binary-coded decimal variant adds 3 to a nibble when converting from binary to BCD in the DAA (decimal adjust) algorithm?
A. Excess-3 only
B. Gray code
C. 8421 BCD adjust uses add-3 when nibble > 9 or carry
D. Two’s complement
33. Which method is used by CRC to detect burst errors effectively?
A. Parity bit
B. Polynomial division modulo 2
C. Weighted checksum
D. Reed-Solomon algorithm
34. The mantissa (fraction) field in normalized IEEE 754 single precision has how many explicit bits (not counting implicit leading 1)?
A. 8
B. 10
C. 23
D. 24
35. What is the main limitation of sign-magnitude arithmetic compared to two’s complement?
A. Simpler hardware
B. Two representations for zero and more complex arithmetic circuits
C. More efficient subtraction
D. No overflow
36. Convert binary 1011₂ to decimal.
A. 9
B. 10
C. 11
D. 12
37. In Booth’s multiplication algorithm, what advantage is exploited?
A. Floating point normalization
B. Runs of 1s are handled with fewer add/subtract operations by encoding bits
C. No shifting required
D. Only works with unsigned numbers
38. Which is true about denormal (subnormal) numbers in IEEE 754?
A. They increase exponent range
B. They allow representation of numbers closer to zero than normalized form permits
C. They have implicit leading 1 in mantissa
D. They always cause exceptions
39. The checksum technique that uses polynomial arithmetic for error detection in network packets is commonly known as:
A. Hamming Check
B. Parity
C. CRC (Cyclic Redundancy Check)
D. Reed-Solomon
40. Converting binary 1110₂ to decimal yields:
A. 6
B. 14
C. 14
D. 13
41. Which of the following is a non-weighted code?
A. 8421 BCD
B. Gray code
C. Excess-3
D. Binary
42. In two’s complement arithmetic with 8 bits, the range of representable integers is:
A. −128 to 127
B. −128 to 127
C. −127 to 128
D. −255 to 255
43. When performing binary subtraction using two’s complement, you should:
A. Subtract magnitudes and keep sign separate
B. Convert to sign-magnitude first
C. Add the minuend and two’s complement of the subtrahend
D. Use 1’s complement
44. Which of the following detects and corrects single-bit errors in data words with minimum redundancy?
A. Parity bit
B. CRC
C. Hamming code
D. SHA checksum
45. For a 32-bit IEEE single-precision float, how many bits are allocated to the exponent?
A. 8
B. 8
C. 11
D. 23
46. What is the binary result of 5 (0101₂) + (−3) in 4-bit two’s complement arithmetic?
A. 0010
B. 0010 (which is +2)
C. 1100
D. Overflow
47. Which representation is preferred for hardware implementation of signed integer arithmetic?
A. Sign-magnitude
B. 1’s complement
C. 2’s complement
D. Excess-3
48. In fixed-point arithmetic, overflow occurs when:
A. Fractional part truncated
B. Integer part exceeds its allotted bit field
C. Exponent becomes too large
D. Mantissa becomes normalized
49. Convert octal 725₈ to decimal.
A. 469
B. 469₁₀
C. 469
D. 501
50. A cyclic redundancy check polynomial of degree r can detect any single-bit error within a transmitted frame of length:
A. r bits
B. Less than r bits only
C. Any frame length, single-bit error always detected
D. Only up to r bits
51. The floating-point operation that results in infinity (and not NaN) is typically:
A. 0/0
B. Infinity − Infinity
C. Nonzero/0
D. sqrt(−1)
52. Which numeric conversion uses repeated division by the target base for the integer part?
A. Fractional multiply method
B. Division-remainder method
C. Complement method
D. Booth’s method
53. The binary representation 0 10000010 10100000000000000000000 (IEEE-754 single) corresponds to which approximate decimal value?
A. 10.5
B. 10.5
C. −10.5
D. 5.25
54. Which of the following is LEAST suitable for detecting multiple random bit errors?
A. CRC with good polynomial
B. Reed-Solomon code
C. Single parity bit
D. Hamming code (with additional parity)
55. In signed arithmetic, overflow can be detected by:
A. Checking carry-out from MSB only
B. Checking sign of operands only
C. Checking whether carry into MSB and carry out of MSB differ
D. Checking zero flag only
56. What is the decimal value of the floating-point bit pattern (single precision) with sign=1, exponent=00000000, fraction=00000000000000000000000?
A. −0 (negative zero)
B. −0 (negative zero)
C. Denormal negative number
D. NaN
57. Which fixed-point format is suitable to represent numbers between −1 and +1 with high fractional precision?
A. Q15.0
B. Q0.15 (or Q1.15 depending on convention)
C. Integer format
D. Exponent-mantissa
58. Which arithmetic algorithm reduces the number of partial products during multiplication by encoding runs of 1s?
A. Karatsuba
B. Booth’s algorithm
C. Wallace tree only
D. Restoring division
59. What is the binary to decimal conversion of fractional binary 0.0011₂?
A. 0.1875
B. 0.1875
C. 0.3125
D. 0.125
60. A CRC is effective at detecting which kind of errors especially?
A. Single-bit errors only
B. Burst errors of length less than or equal to polynomial degree
C. Only odd-number bit errors
D. Only substitution errors
61. Which operation is more problematic in floating-point arithmetic due to rounding errors?
A. Multiplying large numbers
B. Subtracting two nearly equal numbers
C. Adding powers of two
D. Multiplying by zero
62. What does the “biased exponent” allow in IEEE floating-point representation?
A. Represent NaN only
B. Use an unsigned field to store exponent with both positive and negative true exponents
C. Store mantissa sign
D. Reduce mantissa bits
63. Which of the following is true about sign-extension when converting smaller signed integers to larger width in two’s complement?
A. Fill with zeros always
B. Fill with random bits
C. Replicate the sign bit into the new higher-order bits
D. Invert the sign bit
64. Convert decimal 45 to binary.
A. 101101
B. 101101
C. 111001
D. 100101
65. In BCD addition, when a result nibble exceeds 9, what correction is applied?
A. Subtract 6
B. Add 6 (i.e., add 0110₂)
C. Add 9
D. No correction
66. Which of the following is a non-uniform number representation offering more precision near zero?
A. Fixed-point only
B. IEEE floating point normalized only
C. Floating point (due to exponent scaling and denormals)
D. Two’s complement integer
67. The redun¬dancy added by Hamming code for m data bits is approximately:
A. log₂(m)
B. Small r such that 2^r ≥ m + r + 1
C. m/2
D. m + r
68. The result of left-shifting a binary integer by one bit is equivalent to:
A. Dividing by 2
B. Multiplying by 2 (ignoring overflow)
C. Adding one
D. Logical NOT
69. Which of the following detects single-bit errors and can also indicate odd parity?
A. CRC-32
B. Single parity bit (odd/even parity)
C. Hamming code (single-correct)
D. SHA-1
70. Convert binary 10110₂ to octal.
A. 26₈
B. 26₈
C. 16₈
D. 36₈
71. What does “guard bit” mean in floating-point arithmetic units?
A. Extra exponent bit
B. Extra fractional bit(s) used during intermediate rounding to reduce error
C. Sign protection bit
D. Bit indicating overflow
72. The term “normalized” floating-point number means:
A. Exponent is zero
B. Mantissa is adjusted so that the leading digit is non-zero (1 in binary)
C. Fraction is zero
D. Sign is positive
73. Which of the following division algorithms restores the remainder after subtract step if negative?
A. Non-restoring division
B. Restoring division
C. Booth’s division
D. Newton-Raphson
74. In modulo-2 arithmetic for CRC, addition and subtraction are equivalent to:
A. Carry-propagating addition
B. Multiplication
C. XOR operation (bitwise exclusive OR)
D. AND operation
75. Which statement about two’s complement arithmetic is FALSE?
A. It has unique zero.
B. Addition and subtraction use the same hardware.
C. It cannot represent negative numbers.
D. MSB indicates sign.
76. Convert decimal 255 to hexadecimal.
A. FF₁₆
B. FF₁₆
C. FE₁₆
D. 00FF
77. Which of the following is true about excess-K representation?
A. It is another name for two’s complement.
B. Exponent field in floating point often uses excess-K bias to store signed exponents as unsigned
C. It stores magnitude only
D. It is used for mantissa encoding
78. The principle behind parity-check matrix in linear block codes is:
A. Polynomial remainder only
B. Linear algebra: codewords satisfy H·cᵀ = 0 (over GF(2))
C. Hamming distance 1 always
D. Not related to matrices
79. What is the binary representation of decimal -5 in 8-bit two’s complement?
A. 11111011
B. 11111011
C. 11110101
D. 00000101
80. Which floating-point exception corresponds to an operation resulting in a value too small to be represented as a normalized number but non-zero?
A. Overflow
B. Underflow (may produce denormalized number)
C. Division-by-zero
D. Invalid operation
81. In fixed-point multiplication with two Qm.n numbers, the product has:
A. Same Q-format always
B. Sum of fractional bits (n + n) so scaling required to fit original format
C. Exponent adjusted
D. Mantissa increased by one bit
82. Which code minimizes transitions between successive numbers, useful for analog-to-digital encoder interfaces?
A. BCD
B. Gray code
C. Two’s complement
D. Excess-3
83. Convert floating decimal 6.75 into binary floating-point value (integer and fraction parts).
A. 110.11₂
B. 110.11₂
C. 101.11₂
D. 110.101₂
84. In Hamming (7,4) code, how many parity bits are used for 4 data bits?
A. 2
B. 3
C. 4
D. 5
85. When multiplying two’s complement numbers using shift-and-add, one must be careful about:
A. Mantissa alignment
B. Sign extension during shifts and number of bits to represent product
C. Bias correction
D. CRC checks
86. What is the 4-bit Gray code sequence for binary 000, 001, 010, 011 (mapping LSB to MSB straightforwardly)?
A. 0000, 0001, 0011, 0010
B. 0000, 0001, 0011, 0010
C. 0000, 0010, 0011, 0001
D. 0000, 0100, 0101, 0111
87. A floating-point number with exponent field all zeros and non-zero fraction is called:
A. Infinity
B. Denormal (subnormal) number
C. NaN
D. Normalized number
88. Which arithmetic algorithm for division uses successive approximations via reciprocal multiplication to speed up division in floating point hardware?
A. Restoring division
B. Non-restoring division
C. Newton-Raphson or Goldschmidt methods
D. Shift-and-subtract only
89. The typical CRC generator polynomial must not have which factor to detect single-bit errors?
A. (x + 1)
B. x
C. It must not be divisible by x (i.e., should detect single-bit errors: polynomial must have at least two terms)
D. x^n
90. Convert binary fraction 0.101₂ to decimal.
A. 0.625
B. 0.625
C. 0.75
D. 0.5
91. Which representation results in the simplest comparison of signed integers using standard unsigned comparator hardware?
A. Sign-magnitude
B. 1’s complement
C. Two’s complement (comparison works with MSB priority)
D. Excess-3
92. In fixed-point Qm.n, adding two numbers requires:
A. Aligning exponents
B. Same Q-format (same fractional bits) or conversion before addition
C. Changing mantissa length
D. Converting to floating point first
93. Which is the principal cause of round-off error accumulation in repeated floating-point operations?
A. Exact arithmetic
B. Limited precision and rounding at each operation
C. Too many exponent bits
D. Use of integer arithmetic
94. Convert octal 17₈ to binary.
A. 1111₂
B. 001111₂
C. 001111₂ (or 1111₂)
D. 1011₂
95. Which of the following is used to quickly add multi-bit binary numbers in hardware to reduce propagation delay?
A. Ripple-carry adder only
B. Carry-lookahead adder
C. Serial adder only
D. Booth adder
96. The biased exponent 127 in single precision corresponds to an actual exponent of:
A. Always positive 127
B. 0 when stored exponent equals 127
C. −127 when stored exponent is 0
D. 127 only for zeros
97. What is the binary representation (unsigned) of decimal 200?
A. 11001000
B. 11001000
C. 10100000
D. 11110000
98. In error detection, a code’s minimum Hamming distance determines:
A. Only compression ratio
B. Maximum detectable and correctable error counts (detect up to d−1, correct up to ⌊(d−1)/2⌋)
C. Time complexity only
D. Storage requirement only
99. Which operation in binary floating-point needs alignment of significands before execution?
A. Multiplication
B. Division
C. Addition and subtraction
D. Exponent increment
100. What is the main reason for using normalized mantissa (leading 1) in floating-point formats?
A. To complicate hardware
B. To maximize precision by using all available fraction bits
C. To reduce exponent range
D. Because software requires it