Data representation: number systems, fixed and floating point representation, complements, error-detection codes and computer arithmetic algorithms. - Question Bank

1. Which of the following is a method to represent numbers that can be very large or very small with a limited number of bits, sacrificing some precision?
A) Fixed-point representation
B) Integer representation
C) Floating-point representation
D) BCD (Binary Coded Decimal)
2. What is the result of the binary division 1101 / 10?
A) 110 with remainder 1
B) 110 with remainder 0
C) 111 with remainder 0
D) 101 with remainder 1
3. Consider the decimal number 15. What is its representation in one's complement using 8 bits?
A) 00001111
B) 11110000
C) 00001111
D) 10001111
4. What is a 'normalized' floating-point number?
A) A number where the mantissa is zero
B) A number where the leading digit of the mantissa is non-zero
C) A number with a zero exponent
D) A number with a bias applied
5. In Booth's multiplication algorithm, what action is taken when the current and previous bits of the multiplier are '01'?
A) Subtract multiplicand
B) Add multiplicand
C) No operation
D) Shift right
6. What is the primary advantage of using CRC (Cyclic Redundancy Check) over simple parity bits?
A) Simpler implementation
B) Can detect more complex error patterns, including burst errors
C) Requires fewer bits for error checking
D) Faster error detection
7. What does the special exponent value of all 1s in IEEE 754 represent?
A) Zero
B) Infinity or NaN (Not a Number)
C) The smallest representable number
D) The largest representable number
8. What is the bias value used in IEEE 754 single-precision floating-point representation?
A) 127
B) 128
C) 255
D) 256
9. Convert the binary number 111010 to its hexadecimal equivalent.
A) 3A
B) 72
C) 3E
D) 1D
10. Which number system is often used as a shorthand for binary due to its relationship (3 bits per octal digit)?
A) Decimal
B) Hexadecimal
C) Octal
D) Base-3
11. What is the purpose of a 'carry-lookahead adder'?
A) To perform multiplication faster
B) To speed up the addition process by anticipating carries
C) To detect errors in binary numbers
D) To represent floating-point numbers
12. In the context of computer arithmetic, what is an 'overflow'?
A) When the result of an operation is too small to be represented
B) When the result of an operation exceeds the maximum representable value
C) When a division by zero occurs
D) When the sign bit is incorrect
13. What is the result of the binary multiplication 110 * 101?
A) 11110
B) 100010
C) 11111
D) 101110
14. What is the primary goal of using fixed-point representation?
A) To represent a wide range of very large or very small numbers accurately
B) To simplify hardware implementation for arithmetic operations
C) To handle fractional numbers with high precision
D) To reduce memory usage for numbers
15. Which arithmetic algorithm is commonly used for fast multiplication of binary numbers?
A) Restoring Division Algorithm
B) Non-Restoring Division Algorithm
C) Booth's Multiplication Algorithm
D) Addition-Subtraction Algorithm
16. What does the 'guard bit' do in certain arithmetic algorithms?
A) It protects the sign bit
B) It helps in rounding during operations like addition and subtraction
C) It increases the precision of the mantissa
D) It detects overflow conditions
17. What is the typical range of values for the exponent field in IEEE 754 single-precision floating-point representation (before bias)?
A) -127 to 128
B) -128 to 127
C) 0 to 255
D) -255 to 255
18. In the IEEE 754 single-precision floating-point format, how many bits are typically used for the mantissa (significand)?
A) 8
B) 23
C) 1
D) 32
19. In the IEEE 754 single-precision floating-point format, how many bits are typically used for the exponent?
A) 23
B) 8
C) 1
D) 32
20. What is a 'checksum' used for in data communication?
A) To speed up data transmission
B) To compress data
C) To detect errors by summing up data segments
D) To encrypt data
21. If a system uses even parity and transmits the byte 11001010, what would be the parity bit added?
A) 0
B) 1
C) 10
D) Cannot be determined
22. Which of the following binary numbers has an odd number of 1s?
A) 101010
B) 110011
C) 1000001
D) 111100
23. What is the main drawback of one's complement representation?
A) It has two representations for zero (+0 and -0)
B) Arithmetic operations are complex
C) It cannot represent negative numbers
D) It has a limited range
24. In one's complement, how is the negative of a number represented?
A) By inverting all the bits
B) By inverting all the bits and adding 1
C) By subtracting the number from the maximum possible value
D) By appending a sign bit
25. What is the purpose of the 'sign bit' in sign-magnitude representation?
A) To indicate the magnitude of the number
B) To indicate whether the number is positive or negative
C) To represent the fractional part of a number
D) To detect errors in data
26. Which number system uses digits 0-9 and letters A-F?
A) Octal
B) Decimal
C) Binary
D) Hexadecimal
27. What is the decimal value of the octal number 72?
A) 58
B) 64
C) 56
D) 60
28. Perform subtraction using two's complement: 1010 - 0101 (assuming 4-bit representation).
A) 0101
B) 1011
C) 0011
D) 1101
29. What is the result of adding binary numbers 1011 and 0101?
A) 10000
B) 1110
C) 10100
D) 1100
30. Convert the decimal number 25 to its binary representation.
A) 11001
B) 10110
C) 11010
D) 10011
31. Consider the binary number 1101. What is its octal equivalent?
A) 15
B) 13
C) 6
D) 7
32. What is a 'bias' in floating-point representation?
A) A value added to the exponent to ensure it's always positive
B) A value subtracted from the mantissa
C) A special code for zero
D) A technique for error detection
33. What is the range of numbers representable by a fixed-point system limited by?
A) The number of bits allocated for the exponent
B) The number of bits allocated for the mantissa
C) The total number of bits and the position of the binary point
D) The complexity of the arithmetic algorithm
34. Which standard defines the format for floating-point numbers in most modern computers?
A) IEEE 754
B) ASCII
C) EBCDIC
D) ISO 8859
35. What is the 'exponent' in floating-point representation?
A) The significant digits of the number
B) The sign of the number
C) Determines the position of the binary point
D) The base of the number system
36. In floating-point representation, what does the 'mantissa' (or significand) represent?
A) The scale or magnitude of the number
B) The sign of the number
C) The significant digits of the number
D) The exponent
37. What is the primary advantage of using two's complement over sign-magnitude for arithmetic?
A) Simpler representation of zero
B) Eliminates the need for separate addition and subtraction circuits
C) Wider range of representable numbers
D) Easier conversion to hexadecimal
38. If a data stream is 1011001 and an odd parity bit is used, what would be the parity bit?
A) 0
B) 1
C) 2
D) Cannot be determined
39. What is an 'even parity' bit?
A) A bit added to make the total number of 1s odd
B) A bit added to make the total number of 1s even
C) A bit that indicates the sign of the number
D) A bit used in floating-point representation
40. Which of the following is a method used for detecting errors in data transmission or storage?
A) Two's Complement
B) Floating Point Representation
C) Parity Check
D) Sign-Magnitude
41. What is the two's complement representation of -5 in an 8-bit system?
A) 11111011
B) 10000101
C) 00000101
D) 11111010
42. How do you obtain the two's complement of a binary number?
A) Invert all bits
B) Invert all bits and add 1
C) Add 1 to the number
D) Subtract 1 from the number
43. What is the result of the one's complement of the binary number 101101?
A) 010010
B) 010011
C) 101101
D) 001101
44. Which representation method is most commonly used for signed integers due to its efficient arithmetic operations?
A) Sign-Magnitude
B) One's Complement
C) Two's Complement
D) Biased Representation
45. In a fixed-point representation, where is the binary point assumed to be located?
A) Always at the rightmost end of the number
B) Always at the leftmost end of the number
C) Between the most significant bit and the next bit
D) After a predetermined number of bits from the left
46. Which of the following is a common method for representing signed integers in computers?
A) Sign-Magnitude
B) One's Complement
C) Two's Complement
D) All of the above
47. What is the decimal value of the hexadecimal number 3A?
A) 58
B) 60
C) 50
D) 64
48. Convert the binary number 10110 to its decimal equivalent.
A) 18
B) 22
C) 26
D) 30
49. What is the base of the binary number system?
A) 8
B) 10
C) 2
D) 16
50. Which number system is natively used by computers for all internal operations?
A) Decimal
B) Binary
C) Octal
D) Hexadecimal
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