CSE115: Introduction to Number Systems
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CSE115: Introduction to Number Systems

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Questions and Answers

Which base represents the binary number system?

  • 10
  • 8
  • 2 (correct)
  • 16

    • The octal number system uses the symbols 0 to 7.

    True

    What is the value of the hexadecimal number 'A' in decimal?

    10

    A collection of 8 bits is called a ______.

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

    Match the number systems with their base:

    <p>Decimal = 10 Binary = 2 Octal = 8 Hexadecimal = 16</p> Signup and view all the answers

    Which number system is primarily used by humans?

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

    The hexadecimal number system uses symbols beyond 0 to 9.

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

    What two fundamental digits are used in the binary number system?

    <p>0 and 1</p> Signup and view all the answers

    What is the decimal equivalent of the binary number 101011₂?

    <p>43</p> Signup and view all the answers

    The weight for the binary bit furthest to the left is always zero.

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

    What is the method used to convert octal numbers to decimal?

    <p>Multiply each bit by 8 raised to the power of its weight and add the results.</p> Signup and view all the answers

    To convert hexadecimal to decimal, multiply each bit by ____ raised to the power of its weight.

    <p>16</p> Signup and view all the answers

    Match the number system to its base:

    <p>Binary = 2 Decimal = 10 Octal = 8 Hexadecimal = 16</p> Signup and view all the answers

    Which of the following best describes the process of converting decimal to binary?

    <p>Divide by two and keep track of the remainders</p> Signup and view all the answers

    The octal number 724₈ converts to 468₁₀ in decimal.

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

    Calculate the decimal value of the hexadecimal number ABC₁₆.

    <p>2748</p> Signup and view all the answers

    What is the binary representation of the decimal number 117?

    <p>1110101</p> Signup and view all the answers

    What is the octal equivalent of the decimal number 1234?

    <p>2328</p> Signup and view all the answers

    The 10’s complement of 3675 is 6324.

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

    The binary equivalent of the octal number 705 is 111000101.

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

    If the value of 'k' in base 2 is 1024, what does it represent in terms of memory?

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

    The ____’s complement of a number is obtained by subtracting the number from the power of the base.

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

    What is the hexadecimal equivalent of the decimal number 1234?

    <p>4D2</p> Signup and view all the answers

    The binary representation of the hexadecimal number 10AF is ___

    <p>0001000010101111</p> Signup and view all the answers

    Match the following prefixes with their values:

    <p>pico = 10^-12 nano = 10^-9 mega = 10^6 giga = 10^9</p> Signup and view all the answers

    What does the symbol 'M' represent in computing?

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

    Match the following conversion techniques with their descriptions:

    <p>Decimal to Octal = Divide by 8 Decimal to Hexadecimal = Divide by 16 Octal to Binary = Convert each octal digit to binary Hexadecimal to Binary = Convert each hex digit to binary</p> Signup and view all the answers

    What is the octal equivalent of the binary number 10101111?

    <p>257</p> Signup and view all the answers

    The complement of a number is always a positive value.

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

    To convert a binary number to hexadecimal, you group bits in fours.

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

    What is the formula for calculating r’s complement?

    <p>r^n - N</p> Signup and view all the answers

    What is the octal equivalent of the binary number 110110?

    <p>66</p> Signup and view all the answers

    The hexadecimal number 1F0C is equivalent to the octal number ___

    <p>17414</p> Signup and view all the answers

    The result of converting the decimal number 33 to binary is:

    <p>100001</p> Signup and view all the answers

    What is the first step in finding the (r-1)'s complement using the shortcut method?

    <p>Subtract each digit from r-1</p> Signup and view all the answers

    The binary 1's complement requires you to leave the digits unchanged until the first 1 is encountered.

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

    Calculate the 10's complement of (529400)10.

    <p>470600</p> Signup and view all the answers

    (A4D7E0)16 gives r's complement of ______ when calculated.

    <p>5B2820</p> Signup and view all the answers

    Match the numbers with their corresponding r's complements:

    <p>(620143)8 = 1576350 (A4D7E0)16 = 5B2820 (11010010100)2 = 00101101100 (8210)10 = 1790</p> Signup and view all the answers

    Study Notes

    Introduction to Number Systems

    • Base denotes the fundamental symbols in a numbering system (e.g., 0, 1, 2).
    • Common numbering systems include:
      • Decimal (Base 10)
      • Binary (Base 2)
      • Octal (Base 8)
      • Hexadecimal (Base 16)

    Common Number Systems

    • Decimal (Base 10): Used by humans, symbols 0-9, not used by computers.
    • Binary (Base 2): Symbols 0, 1; used by computers, not by humans.
    • Octal (Base 8): Symbols 0-7; not used commonly, useful for representing long binary numbers.
    • Hexadecimal (Base 16): Symbols 0-9, A-F; also useful for representing long binary numbers.

    Counting in Different Bases

    • Values of decimal, binary, octal, and hexadecimal representations are established.
    • Example conversions show a range from 0 to 20.

    Bits and Bytes

    • A bit is the smallest unit in binary, while a byte is a collection of 8 bits.
    • Binary system consists of two digits: 0 and 1.

    Conversion Among Bases

    • Techniques for converting between decimal, binary, octal, and hexadecimal systems are highlighted.
    • For decimal representation, the weight or position of the digit affects its value exponentially based on the base.

    Binary to Decimal Conversion

    • Multiply each bit by 2 raised to the bit's position (weight).
    • Sum all values to get the decimal equivalent.

    Octal to Decimal Conversion

    • Multiply each octal digit by 8 raised to its position.
    • Add the results for the decimal output.

    Hexadecimal to Decimal Conversion

    • Multiply each hexadecimal digit by 16 raised to its position.
    • Sum the products to convert into decimal.

    Decimal to Binary Conversion

    • Divide the decimal number by 2, recording remainders.
    • The sequence of remainders gives the binary representation.

    Decimal to Octal Conversion

    • Divide the decimal number by 8, keeping track of remainders.
    • The remainders will form the octal output.

    Decimal to Hexadecimal Conversion

    • Divide the decimal number by 16 and track the remainders.
    • The sequence will give the hexadecimal representation.

    Octal to Binary Conversion

    • Convert each octal digit into its 3-bit binary equivalent.

    Binary to Octal Conversion

    • Group binary digits in sets of three, converting each group to an octal digit.

    Hexadecimal to Binary Conversion

    • Convert each hexadecimal digit to its 4-bit binary equivalent.

    Binary to Hexadecimal Conversion

    • Group bits in sets of four and convert each group to a single hexadecimal digit.

    Octal to Hexadecimal and Vice Versa

    • Use binary as a bridge for conversion between octal and hexadecimal formats.

    Common Powers of 10 and 2

    • Base 10 prefixes include pico, nano, micro, milli, kilo, mega, giga, and tera with respective values.
    • Base 2 prefixes like kilo, mega, and giga have specific values relevant in computing.

    Complement

    • The complement of a number provides its negative equivalent.
    • Two types of complements exist for a base: r's complement and (r-1)'s complement.

    Finding r’s and (r-1)’s Complements

    • r’s complement of a number is found using the formula r^n - N.
    • (r-1)’s complement is calculated as r^n - N - 1.
    • Shortcuts exist for finding complements, simplifying the process, especially in binary.

    Examples of Complement Calculations

    • Various examples illustrate how to compute complements in different bases using both the standard method and shortcuts, demonstrating practical applications.

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    Related Documents

    CSE115Lecture01NumberSystems.pptx

    Description

    This quiz covers the basics of numbering systems as introduced in Lecture 01 of CSE115: Computing Concepts. Students will explore different bases, including binary, octal, and hexadecimal, along with their significance and applications in computing.

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