Binary Numbers and Conversion Techniques
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Questions and Answers

What is the maximum decimal number that can be represented by a 4-digit octal number?

  • 511
  • 2048
  • 777
  • 4095 (correct)

    • What is the octal equivalent of the binary number 001101010111001111?

  • 177512
  • 152717 (correct)
  • 153721
  • 152417

    • How many bits are used to represent a single octal digit?

  • 3 (correct)
  • 4
  • 5
  • 2

    • Which of the following statements is true about the octal numbering system?

    <p>Octal counting restarts after 8.</p> Signup and view all the answers

    What is the decimal equivalent of the octal number 6717?

    <p>35310</p> Signup and view all the answers

    What is the decimal equivalent of the binary number 101?

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

    Which binary representation corresponds to the decimal number 6?

    <p>110</p> Signup and view all the answers

    How many bits are there in one byte?

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

    Identify the Most Significant Bit (MSB) position in the binary number 10110010.

    <p>7</p> Signup and view all the answers

    What is the sum of the binary bits in 10000 when converted to decimal?

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

    In binary representation, how is the decimal number 9 expressed?

    <p>1001</p> Signup and view all the answers

    What is indicated by a group of 4 bits?

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

    What is the binary equivalent of the decimal number 50?

    <p>101010</p> Signup and view all the answers

    Which base is commonly used for digital computers due to the simplicity of using two values?

    <p>Binary (base-2)</p> Signup and view all the answers

    What is the decimal equivalent of the binary number 11111111?

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

    What happens when converting the number 1024 into binary?

    <p>10000000000</p> Signup and view all the answers

    Which method is commonly used to convert a decimal number to its binary equivalent?

    <p>Division by 2 method</p> Signup and view all the answers

    When converting the decimal number 99 to binary, what is the least significant bit (LSB)?

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

    What base is used to represent memory addresses and OP-Codes in a more compact form?

    <p>Hexadecimal (base-16)</p> Signup and view all the answers

    How many binary digits are combined to form one octal digit?

    <p>3</p> Signup and view all the answers

    What is the maximum decimal value that can be represented by a single hexadecimal digit?

    <p>15</p> Signup and view all the answers

    If the binary number 110111001111 is grouped into nibbles, what is the hexadecimal equivalent?

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

    How many unique values can be represented in a byte using hexadecimal digits?

    <p>256</p> Signup and view all the answers

    Which hexadecimal digits are used to represent decimal values from 10 to 15?

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

    How is the hexadecimal system related to the binary system?

    <p>Hexadecimal represents 4 bits with one digit.</p> Signup and view all the answers

    Which decimal number corresponds to the hexadecimal digit 'C'?

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

    When converting the binary number 110111001111 to decimal, what is the total value calculated?

    <p>3535</p> Signup and view all the answers

    What is the fundamental base of the hexadecimal numbering system?

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

    What is the decimal equivalent of the hexadecimal number F8?

    <p>248</p> Signup and view all the answers

    Which of the following binary numbers correctly represents E75 in hexadecimal?

    <p>111001110101</p> Signup and view all the answers

    What is the hexadecimal representation of the decimal number 1128?

    <p>468</p> Signup and view all the answers

    How would you express the binary number 101110111 in hexadecimal?

    <p>B7</p> Signup and view all the answers

    Which of the following correctly converts 64 from decimal to hexadecimal?

    <p>40</p> Signup and view all the answers

    What is the decimal value of the hexadecimal number 57A?

    <p>1398</p> Signup and view all the answers

    What is the binary equivalent of the hexadecimal number EFC?

    <p>111011111100</p> Signup and view all the answers

    Which of the following correctly describes the characteristic of octal numbers?

    <p>An octal number uses digits from 0 to 7.</p> Signup and view all the answers

    How can a binary number that does not have a multiple of four bits be converted to hexadecimal?

    <p>Add additional zeros to the left</p> Signup and view all the answers

    If a binary number is 110110101101, what would be its hexadecimal equivalent after proper grouping?

    <p>D5</p> Signup and view all the answers

    What is the maximum decimal value that can be represented by a 4-digit hexadecimal number?

    <p>65,535</p> Signup and view all the answers

    What is the hexadecimal representation of the binary number 11101010?

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

    How many hexadecimal digits are needed to represent the decimal number 256?

    <p>3</p> Signup and view all the answers

    What is the result when converting the hexadecimal number 3FA7 into binary?

    <p>0011 1111 1010 0111</p> Signup and view all the answers

    What is the significance of counting in hexadecimal compared to binary and decimal?

    <p>Hexadecimal requires fewer digits to represent a number</p> Signup and view all the answers

    Study Notes

    Binary Numbers

    • Digital systems process, store, and transmit data efficiently using discrete values.
    • The binary number system (base-2) uses only 0 and 1.
    • A binary digit (0 or 1) is called a bit.
    • Eight bits form a byte.
    • A nibble is a group of four bits.
    • Binary numbers are a series of bits, each weighted by increasing powers of 2, from right to left.
    • The most significant bit (MSB) is the leftmost bit.
    • The least significant bit (LSB) is the rightmost bit.
    • Example: 10110010₂ = 178₁₀

    Decimal to Binary Conversion

    • Divide the decimal number by 2 repeatedly.
    • Record the remainders.
    • The remainders, read from the last to first, form the binary equivalent.
    • Example: 157₁₀ = 10011101₂

    Binary to Decimal Conversion

    • Multiply each bit by its corresponding power of 2.
    • Sum the results to get the decimal equivalent.
    • Example: 101101₂ = (1 × 2⁵) + (0 × 2⁴) + (1 × 2³) + (1 × 2²) + (0 × 2¹) + (1 × 2⁰) = 45₁₀

    Hexadecimal System

    • Groups of four bits in a binary number represent a single hexadecimal digit.
    • Hexadecimal uses digits 0-9 and letters A-F to represent values from 0 to 15.
    • A hexadecimal number is easier to read and write than a long binary number.

    Octal System

    • Groups of three bits in a binary number represent a single octal digit.
    • Octal uses digits 0-7 to represent values from 0 to 7.
    • Octal is also a shorthand representation for binary numbers.

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    Binary Numbers PDF

    Description

    This quiz explores the binary number system, including its structure, conversion between decimal and binary formats, and the hexadecimal system. Understanding these concepts is crucial for working with digital systems that process and transmit data. Test your knowledge and improve your skills in binary numbers and conversions.

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