Computer Science Chapter 2: Data Representation
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Questions and Answers

What is the range of values for an unsigned 16-bit integer?

  • 0 to 255
  • 0 to 65,535 (correct)
  • 0 to 4,294,967,295
  • -32768 to 32767

    • How many bytes are used to represent a 64-bit word?

  • 8 bytes (correct)
  • 2 bytes
  • 4 bytes
  • 1 byte

    • What does a value of 1 in the most-significant bit indicate in the sign-magnitude bit model?

  • A negative number (correct)
  • An unsigned value
  • A positive number
  • Zero

    • In the magnitude-only bit model, which range corresponds to a single byte?

    <p>0 to 255</p> Signup and view all the answers

    How is the highest positive number represented in a single byte using the sign-magnitude bit model?

    <p>01111111</p> Signup and view all the answers

    What is the main disadvantage of the sign-magnitude bit model?

    <p>It has a smaller magnitude range.</p> Signup and view all the answers

    What is the conversion of the binary number 10000010 in the sign-magnitude model?

    <p>-2</p> Signup and view all the answers

    When using a sequence of 4 bytes to represent numbers, what is the maximum number that can be represented?

    <p>4,294,967,295</p> Signup and view all the answers

    What is the primary reason for understanding how data is represented in a computer?

    <p>To correctly interpret the binary data</p> Signup and view all the answers

    Which bit model allows representation of both positive and negative numbers?

    <p>Two's complement</p> Signup and view all the answers

    What constitutes the core unit of data in all digital systems?

    <p>Bit</p> Signup and view all the answers

    How can the sequence of bits '01000011 01001111 01010111' be interpreted in one way?

    <p>As a sequence of characters</p> Signup and view all the answers

    What is the significance of using different number systems such as Hexadecimal, Octal, and Binary in computing?

    <p>They provide varying representation formats for data</p> Signup and view all the answers

    Which compound data type is NOT typically used in the context of data representation?

    <p>Integers</p> Signup and view all the answers

    What operation allows the representation of the decimal number '62389' to be understood in the binary system?

    <p>Base conversion techniques</p> Signup and view all the answers

    Which statement correctly represents the operation of converting a decimal number to binary?

    <p>Dividing by 2 repeatedly and recording remainders</p> Signup and view all the answers

    What is the magnitude of -19 when converted to its two's complement representation?

    <p>19</p> Signup and view all the answers

    What occurs when two positive numbers are added together and the result is negative?

    <p>An overflow has occurred</p> Signup and view all the answers

    What is the range of a signed short int in C?

    <p>-32,768 to 32,767</p> Signup and view all the answers

    When adding two negative numbers in two's complement, which situation represents an overflow?

    <p>The result is positive</p> Signup and view all the answers

    How many bytes does a signed long use in C?

    <p>8 bytes</p> Signup and view all the answers

    What is the purpose of the standard ASCII code?

    <p>To represent non-accented English text characters and punctuations in numeric format.</p> Signup and view all the answers

    How many bytes does each character take in the standard ASCII representation?

    <p>1 byte</p> Signup and view all the answers

    What happens to unsigned char values above 127 when stored?

    <p>They become negative</p> Signup and view all the answers

    If the result of an addition operation in two's complement is represented by the pattern 10000101, what can be inferred?

    <p>The result is a negative number</p> Signup and view all the answers

    Which data type in C uses two's complement for its representation?

    <p>signed char</p> Signup and view all the answers

    What encoding scheme is most commonly used to represent Unicode characters?

    <p>UTF-8</p> Signup and view all the answers

    What is the maximum value that can be represented by a signed char in C?

    <p>127</p> Signup and view all the answers

    In the given context, how many bits are typically used to represent boolean values for customers' logged-on status?

    <p>8 bits</p> Signup and view all the answers

    What is described as a waste of storage space when tracking boolean values?

    <p>Storing each boolean in its own byte.</p> Signup and view all the answers

    How can multiple log-on statuses be efficiently stored in memory?

    <p>Storing 8 booleans in a single byte.</p> Signup and view all the answers

    How many characters can UTF-8 representation take up to in bytes?

    <p>4 bytes</p> Signup and view all the answers

    What is the general form used to express a number in scientific notation?

    <p>± M x BE</p> Signup and view all the answers

    How many bits are used for the mantissa in the float data type in C?

    <p>23</p> Signup and view all the answers

    What bias is added to the exponent in the IEEE 754 32-bit floating-point standard?

    <p>127</p> Signup and view all the answers

    In the IEEE 754 32-bit floating-point representation, what does a 1-bit sign of '0' indicate?

    <p>The number is positive</p> Signup and view all the answers

    What is the bit representation of positive infinity in the IEEE 754 format?

    <p>0 11111111 00000000000000000000000</p> Signup and view all the answers

    Which special case is represented by a mantissa that is non-zero in the IEEE 754 format?

    <p>NaN</p> Signup and view all the answers

    For double-precision numbers, what is the bias used for the exponent?

    <p>1023</p> Signup and view all the answers

    What is the total number of bits used to represent a double data type in C?

    <p>64</p> Signup and view all the answers

    What is the decimal value of the binary number 1001101?

    <p>77</p> Signup and view all the answers

    Which characters are used in the hexadecimal number system?

    <p>0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F</p> Signup and view all the answers

    What will be the decimal equivalent of the octal number 113?

    <p>75</p> Signup and view all the answers

    Which of the following calculations correctly represents the conversion of 1001101 to decimal?

    <p>(1<em>20) +(0</em>21) +(1<em>22) +(1</em>23) +(0<em>24) +(0</em>25) +(1*26)</p> Signup and view all the answers

    In the provided C code, what is the value of the unsigned char hex2 variable after execution?

    <p>2989</p> Signup and view all the answers

    How many digits are used in the octal number system?

    <p>8</p> Signup and view all the answers

    When converting a decimal number to binary, what is the maximum digit that can be used?

    <p>1</p> Signup and view all the answers

    What is the base of the Decimal number system?

    <p>10</p> Signup and view all the answers

    Study Notes

    Chapter 2: Data Representation

    • Data in memory is represented numerically
    • Data is ultimately stored as 1s and 0s
    • Understanding how data is stored is crucial to correct interpretation
    • Example data: 01000011 01001111 01010111 can be interpreted in various ways

    Number Representation and Bit Models

    • Data representation in computers is numerical, even if the initial data is text or image
    • The decimal system (base 10) is used in normal calculations
    • Number systems used in computer science include:
      • Binary (base 2): Uses 0 and 1
      • Octal (base 8): Uses 0-7
      • Decimal (base 10): Uses 0-9
      • Hexadecimal (base 16): Uses 0-9 and A-F
    • Conversion between number systems is possible using the base as a multiplicative factor

    Base Conversion Methods

    • Conversion from binary to decimal, octal, and hexadecimal is explained
    • Conversion from other bases to decimal is explained

    Bit Models

    • Magnitude-only: Represents non-negative numbers. Each bit corresponds to a power of 2. (e.g., 8-bit value can store 0-255)
    • Sign-magnitude: Uses the most significant bit for the sign (+ or -). Numbers in the -127 to +127.
    • Two's complement: Represents both positive and negative numbers using a similar approach to represent negative values as the negative two's complement (+0 is 00...0 and -0 is 11...1). Numbers in the -128 to +127 range.
    • Fixed-point: Represents numbers with a binary point that separates integer and fractional parts. Precision and range are limited.
    • Floating-point: Represents numbers in scientific notation for high precision and range. Exponents and mantissas are combined into a fixed-width representation.

    C Data Types and Bit Usage

    • C data types (unsigned char, unsigned short int, unsigned int, unsigned long int) with bit usage and corresponding ranges
    • Signed data types (char, short int, int, long int) with their respective bit usage and ranges
    • ASCII and Unicode Bit Models: Used for representing characters and text through mapping to numerical values

    Bitwise Operations

    • Basic bitwise operators (~, &, |, ^, >>, <<) in C, and the operations they perform on bits (inversion, AND, OR, XOR, right-shift, left-shift)

    Compound Data Types

    • Strings and char Arrays: Arrays of characters that store sequences of characters, terminated by a null character (\0). Length is not explicitly stored.
    • Arrays: Store multiple values of the same data type sequentially
    • Structures: Combine different data types into a single unit, often representing complex objects (e.g., a person's address). Each member has a distinct location in memory.
    • Unions: Allow different data types to occupy the same memory location. Only one member can be valid at a time.

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    COMP2401 Chapter 2 - Data Representation PDF

    Description

    This quiz focuses on Chapter 2, which examines data representation in computers. It covers the various number systems, conversion methods, and how data is ultimately stored in memory. Understanding these concepts is essential for interpreting data accurately in computing.

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