Binary Subtraction and 2's Complement Methods
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Questions and Answers

What is the result of the subtraction 11010 – 10000 using the 2’s complement method?

  • -16
  • +10 (correct)
  • +16
  • -10

    • In the subtraction 11010 – 1101, what does the carry bit indicate?

  • The result is positive. (correct)
  • The result is negative.
  • The carry should be included in the final result.
  • The first number is larger.

    • What is the outcome of 100 – 110000 using 2’s complement?

  • -48
  • -44 (correct)
  • +48
  • +44

    • What does an MSB (most significant bit) of 1 in the result signify?

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

    When performing binary subtraction using the 2's complement method, why do we ignore the carry?

    <p>It doesn't affect the MSB.</p> Signup and view all the answers

    What is the interpretation of the result when the result's MSB is 0 after performing binary subtraction?

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

    What is the binary representation of the decimal number 13?

    <p>1101</p> Signup and view all the answers

    Which binary number is equivalent to the decimal number 27?

    <p>10111</p> Signup and view all the answers

    In binary counting, how many numbers can be represented with 5 bits?

    <p>32</p> Signup and view all the answers

    What is the next binary number after 1111 in sequential counting?

    <p>10000</p> Signup and view all the answers

    How many bits are needed to represent the decimal number 39 in binary?

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

    Which of the following statements about binary representation is true?

    <p>The rightmost bit alternates between 0 and 1.</p> Signup and view all the answers

    What is the significant pattern observed in binary numbers when counting?

    <p>Each column has increasing groups of alternating zeros and ones.</p> Signup and view all the answers

    What is the result of the subtraction operation 11010 - 10000 using 1's complement method?

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

    When subtracting 11010 - 1101 using 1's complement, what is the final result?

    <p>+13</p> Signup and view all the answers

    In the operation 100 - 110000, which of the following statements is correct regarding its 1's complement subtraction?

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

    What does the final result of 1010100 - 1010100 equal to when computed using the 1's complement method?

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

    In a 16-bit computer, what is the range of expressible integer values?

    <p>From -32768 to +32767</p> Signup and view all the answers

    What happens when there is no carry in the subtraction of binary numbers?

    <p>The MSB determines if the result is positive or negative.</p> Signup and view all the answers

    In the subtraction of 11010 - 10000, how is the 1's complement of the subtrahend represented?

    <p>01111</p> Signup and view all the answers

    Which process is used to determine the final result when the MSB indicates a negative outcome?

    <p>Taking the 1's complement of the result.</p> Signup and view all the answers

    What is the base or radix of the octal system?

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

    Why is the octal system considered convenient for expressing binary numbers?

    <p>It represents binary numbers in a shorter length.</p> Signup and view all the answers

    In what way can octal numbers be useful in computer science?

    <p>They simplify the representation of large binary numbers.</p> Signup and view all the answers

    Which of the following statements about the octal and binary systems is false?

    <p>Octal is only useful for numerical data representation.</p> Signup and view all the answers

    What role do octal numbers play when binary numbers are not representing numerical quantities?

    <p>They convey non-numerical information.</p> Signup and view all the answers

    What result do you get when subtracting 1 from 10 in the 2–2's column?

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

    What happens when you attempt to subtract a 1 from a 0 in the binary system?

    <p>You cannot perform the operation without borrowing</p> Signup and view all the answers

    During the borrowing process in binary subtraction, what value is left in the 2's column after borrowing from the 4's column?

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

    When using the paper method for binary multiplication, what happens if the multiplier bit is a 0?

    <p>You write a 0 as the partial product</p> Signup and view all the answers

    In the binary multiplication example provided, what is the first partial product when multiplying 1101 by 110?

    <p>0000</p> Signup and view all the answers

    Which statement correctly describes binary multiplication of 1 ¥ 1?

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

    How do you derive the final answer in binary multiplication using the paper method?

    <p>Add the partial products</p> Signup and view all the answers

    After completing the binary multiplication of 1101 by 110, what would the final result be?

    <p>1001110</p> Signup and view all the answers

    What is the octal equivalent of the decimal number 10?

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

    Which of the following binary groups corresponds to the octal digit 5?

    <p>101</p> Signup and view all the answers

    How do you convert an octal number to binary?

    <p>Replace each octal digit with its 3-bit binary equivalent.</p> Signup and view all the answers

    What is the binary equivalent of the octal number 17?

    <p>011101</p> Signup and view all the answers

    To convert the binary number 101011.011 to octal, what is the first step?

    <p>Group the binary into blocks of 3 bits.</p> Signup and view all the answers

    What is the result of converting the octal number 36 to binary?

    <p>011110</p> Signup and view all the answers

    What would be the octal representation of the binary number 110101.010?

    <p>65.5</p> Signup and view all the answers

    In the octal system, what is the decimal number that corresponds to the octal representation of 24?

    <p>20</p> Signup and view all the answers

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