Binary and Number Systems Quiz
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Questions and Answers

What is the first step in converting a decimal number to binary?

  • Divide the decimal number by 2. (correct)
  • Write down the decimal number as it is.
  • Add 1 to the decimal number.
  • Multiply the decimal number by 2.

    • How do you obtain the binary equivalent after calculating the remainders?

  • Arrange the remainders in the same order they were obtained.
  • Arrange the remainders in ascending order.
  • Write the remainders in reverse order. (correct)
  • Add all the remainders together.

    • Which of the following is a valid representation for the decimal number 657 in binary?

  • 1010010001 (correct)
  • 1011010110
  • 0110101001
  • 1101011001

    • What base does the octal number system use?

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

    In the binary multiplication table, what is the result of 1 multiplied by 1?

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

    What symbols are used in the hexadecimal number system?

    <p>0 to 9 and A to F</p> Signup and view all the answers

    Which decimal number is equivalent to the hexadecimal symbol 'C'?

    <p>12</p> Signup and view all the answers

    When converting the decimal number 987 to binary, what is the last remainder obtained?

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

    What is the decimal equivalent of the binary number (1011)2?

    <p>11</p> Signup and view all the answers

    What is the decimal equivalent of the binary number (100110)2?

    <p>38</p> Signup and view all the answers

    When adding the binary numbers (10101)2 and (00111)2, what is the result?

    <p>(11101)2</p> Signup and view all the answers

    What is the result of subtracting the binary number (01010)2 from (10011)2?

    <p>(01001)2</p> Signup and view all the answers

    What is the product of the binary numbers (101)2 and (011)2?

    <p>(1111)2</p> Signup and view all the answers

    What is the result of multiplying (1011)2 by (101)2?

    <p>(111001)2</p> Signup and view all the answers

    What is the decimal equivalent of the binary number (10101)2?

    <p>21</p> Signup and view all the answers

    What is the outcome of subtracting (001)2 from (111)2?

    <p>(100)2</p> Signup and view all the answers

    What is the base of the Binary number system?

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

    Which digits are used in the Hexadecimal number system?

    <p>0 to 9 and A to F</p> Signup and view all the answers

    In Binary subtraction, what is the result of 1 - 1?

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

    Which of the following statements is true regarding the Decimal number system?

    <p>It uses the digits from 0 to 9.</p> Signup and view all the answers

    Who introduced the concept of zero?

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

    When converting a Decimal number to Binary, by which number is the Decimal number divided?

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

    In Binary multiplication, what is 1 multiplied by 0?

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

    What is the significance of the right-most digit in a number?

    <p>Least Significant Digit</p> Signup and view all the answers

    Study Notes

    Decimal to Binary Conversion

    • Divide the decimal number by 2, noting the remainder.
    • Continue dividing the quotient by 2 and recording remainders.
    • Repeat until the quotient reaches zero.
    • Reverse the order of remainders to obtain the binary equivalent.

    Binary Multiplication Rules

    • Follows the same principles as decimal multiplication.
    • Multiplication outcomes:
      • 0 * 0 = 0
      • 0 * 1 = 0
      • 1 * 0 = 0
      • 1 * 1 = 0 with a carry of 1.

    Octal Number System

    • Consists of eight digits: 0 to 7.
    • Based on base 8.
    • Originated from Native American counting methods using finger spacing.

    Hexadecimal Number System

    • Comprises 16 symbols: 0-9 and A-F.
    • Represents decimal values as follows:
      • A = 10, B = 11, C = 12, D = 13, E = 14, F = 15.
    • Based on base 16.

    Decimal to Binary Conversion Examples

    • 68 in decimal:
      • Binary equivalent is 1000100 (2).
    • 987 in decimal:
      • Binary equivalent is 1111011011 (2).
    • 657 in decimal:
      • Binary equivalent is 1010010001 (2).

    Binary to Decimal Conversion Examples

    • (1011)₂ = 11 (10).
    • (100110)₂ = 38 (10).
    • (10101)₂ = 21 (10).

    Binary Addition Examples

    • 10101 + 00111 = 11100.
    • 1000101101 + 1001101 = 1001001110.
    • 1101 + 1001 = 10110.

    Binary Subtraction Examples

    • 10011 - 01010 = 01001.
    • 11001001 - 01100110 = 11000011.
    • 111 - 001 = 110.

    Binary Multiplication Examples

    • 101 * 011 = 1111.
    • 1011 * 101 = 1101111.
    • 101010 * 1011 = 111001110.

    Recap of Number Systems

    • Decimal: Base 10, digits 0-9.
    • Binary: Base 2, digits 0-1.
    • Octal: Base 8, digits 0-7.
    • Hexadecimal: Base 16, digits 0-9 and A-F.

    Important Definitions

    • Least Significant Digit: Rightmost digit in a number.
    • Most Significant Digit: Leftmost digit in a number.

    Fill in the Blanks

    • The base of the Binary number system is 2.
    • The base of the Decimal number system is 10.
    • Octal number system uses 8 digits.
    • Binary numbers are used by computers.
    • Hexadecimal includes 0-9 and A-F.
    • In Binary subtraction, 1 - 1 = 0.

    True or False Statements

    • Arithmetic operations can be performed on binary numbers: False.
    • Decimal system involves digits 0 to 9: True.
    • Binary division is similar to decimal: False.
    • 1 multiplied by 0 equals 0: True.
    • Valid digits in Octal range from 1 to 7: False.

    Multiple Choice Questions

    • Zero was conceptualized by b) Aryabhata.
    • C in hexadecimal represents c) 12.
    • Computers understand c) Binary code.
    • In binary multiplication, 1 * 1 equals b) 1.
    • Decimal to binary conversion involves division by a) 2.

    Number System Definition

    • Represents values for various quantities (e.g., counting, statistics).

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    Related Documents

    Class 7 Computer Chapter 1 Answers PDF

    Description

    Test your knowledge on converting decimal numbers to binary and other number systems. This quiz covers important concepts such as binary multiplication, octal bases, and hexadecimal symbols. Perfect for students studying number systems in mathematics.

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