Number Systems and Conversions Quiz
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Questions and Answers

What is the binary representation of the exponent E when converting the number 0.000000110110100101 to IEEE 754 format?

  • (01111100)2
  • (01111010)2
  • (01111110)2
  • (01111000)2 (correct)
  • In the IEEE 754 format for the number 0.000000110110100101, what is the sign bit?

  • 2
  • Negative
  • 1
  • 0 (correct)
  • How many zeros are added to the fraction part when converting the number to IEEE 754 format?

  • 12 (correct)
  • 10
  • 15
  • 20
  • What does the equation E - 127 = -7 represent in the context of converting to IEEE 754 format?

    <p>Determining the biased exponent.</p> Signup and view all the answers

    What is the common binary code representation used for decimal digits in internal arithmetic computations?

    <p>Binary Coded Decimal (BCD)</p> Signup and view all the answers

    What does control information represent in a computer's memory or processor registers?

    <p>A bit or group of bits for command signals</p> Signup and view all the answers

    Which of the following is NOT a digit in the decimal number system?

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

    What is the decimal equivalent of the binary number (101101)2?

    <p>61</p> Signup and view all the answers

    Which radix system is represented by the symbols 0-7?

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

    Which are the symbols used in the hexadecimal number system?

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

    When converting from radix r to decimal, what is the process used?

    <p>Summing up weighted digits</p> Signup and view all the answers

    In a binary number system, how many distinct symbols are used?

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

    Which of the following correctly identifies the components of a number system of base r?

    <p>A sequence of specific symbols</p> Signup and view all the answers

    What is r’s complement of a number N?

    <p>rn - N</p> Signup and view all the answers

    What indicates that an overflow has occurred when adding two binary numbers?

    <p>The carry into the sign bit differs from the carry out of the sign bit.</p> Signup and view all the answers

    Which of the following statements about floating-point binary representation is true?

    <p>It operates similarly to decimal representation.</p> Signup and view all the answers

    How do you convert a binary number such as (10.01101)2 to decimal?

    <p>Use descending negative powers of two to the right of the decimal point.</p> Signup and view all the answers

    What occurs when the addition of two n-digit numbers results in n + 1 digits?

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

    If the binary addition of two positive numbers results in a negative outcome, what can be inferred?

    <p>An error occurred due to the overflow.</p> Signup and view all the answers

    Which of the following describes a component of binary representation?

    <p>Each bit position corresponds to a power of two.</p> Signup and view all the answers

    What would be the decimal value of the binary number (00110101)2?

    <p>53</p> Signup and view all the answers

    What does the left-most bit in Signed-Magnitude representation indicate?

    <p>The sign of the integer</p> Signup and view all the answers

    What is the BCD representation for the decimal number 9?

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

    In signed-magnitude arithmetic, what must you do if the signs of the two operands differ?

    <p>Determine which operand has the larger magnitude and subtract accordingly</p> Signup and view all the answers

    Which binary code uses 7 bits to represent 128 characters?

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

    What is the mathematical range of integers represented in N-bits using Signed-Magnitude?

    <p>From $-(2^{(N-1)} - 1)$ to $(2^{(N-1)} - 1)$</p> Signup and view all the answers

    What characterizes an Overflow in signed numbers during arithmetic operations?

    <p>Adding two operands results in an incorrect sign</p> Signup and view all the answers

    What is one limitation of both ASCII and EBCDIC?

    <p>They are not suitable for non-Latin alphabets.</p> Signup and view all the answers

    Which method is used for simplifying subtraction operations in digital computers?

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

    How many bits does Unicode use to encode a majority of the world's characters?

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

    How are the ranges of integers represented in radix r systems defined?

    <p>With both r’s complement and (r-1)'s complement</p> Signup and view all the answers

    Which of the following best describes BCD?

    <p>It encodes each decimal digit in a separate group of bits.</p> Signup and view all the answers

    What operation is primarily simplified by using complements in binary systems?

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

    What is the basic principle when performing addition in Signed-Magnitude if both signs are the same?

    <p>Add the magnitudes and use the same sign</p> Signup and view all the answers

    What does EBCDIC stand for?

    <p>Extended Binary Coded Decimal Interchange Code</p> Signup and view all the answers

    Which of the following statements about Unicode is true?

    <p>It can encode characters from multiple languages.</p> Signup and view all the answers

    What is the purpose of the sign bit in IEEE Standard 754 floating-point formats?

    <p>To indicate whether the number is positive or negative</p> Signup and view all the answers

    In the equation for single-precision floating-point representation, what does 'E' represent?

    <p>The exponent in binary representation</p> Signup and view all the answers

    What is the decimal value of the exponent E for the binary value 10101101?

    <p>173</p> Signup and view all the answers

    Which condition represents positive infinity in IEEE Standard 754 representation?

    <p>E=255 and F=0</p> Signup and view all the answers

    What is the binary result after converting the single-precision IEEE Standard 754 number 11010110101101101011000000000000?

    <p>-1.01101101011000000000000 x 2^(173-127)</p> Signup and view all the answers

    How is the binary point positioned in the IEEE floating-point representation?

    <p>It is implied before the fraction part F</p> Signup and view all the answers

    In creating the IEEE Standard 754 representation, what exponent is used when the decimal point is moved seven positions to the right?

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

    Which of the following conditions represents zero in IEEE Standard 754 representation?

    <p>E=0 and F=0</p> Signup and view all the answers

    Study Notes

    Number Systems and Codes

    • Data types in computer memory and registers include: numbers for arithmetic, letters for processing, and other discrete symbols.
    • A number system with base r (radix r) uses r distinct symbols or digits.
    • The decimal system (radix 10) uses digits 0 through 9.
    • The binary system (radix 2) uses digits 0 and 1.
    • The octal system (radix 8) uses digits 0 through 7.
    • The hexadecimal system (radix 16) uses digits 0 through 9 and letters A through F.

    Number System Conversions

    • Decimal to other systems: Separate the integer and fractional parts, convert each part individually. For integers, successive divisions by the desired radix and accumulating remainders are used. For fractions, successive multiplications by the radix and accumulating integer parts are used.
    • Other systems to decimal: Use the weighted sum method. Each digit is multiplied by the corresponding power of the radix and all results are summed. For example, (736.4)8 = (7 * 82) + (3 * 81) + (6 * 80) + (4 * 8-1) = 478.510

    Signed-Integer Representation

    • Methods for representing signed integers in computers:
      • Signed-magnitude: The leftmost bit represents the sign (0 for positive, 1 for negative), and the remaining bits represent the magnitude.
      • r-1's complement: Used for simplifying subtraction. The (r-1)'s complement of a number N, in base r with n digits, is (r^n - 1) - N
      • r's complement: rn-N if N is not zero, 0 if N is zero
    • Overflow: Occurs when the result of an arithmetic operation is larger or smaller than the maximum or minimum value that can be represented in the given format.

    Complements

    • (r-1)'s complement: The result of subtracting a number from the largest representable number in a system (1's complement if base 2)

    • r's complement: The result of adding 1 to the (r-1)'s complement.

    Floating-Point Binary

    • Floating-point numbers represent real numbers using an exponent and fractional part (mantissa) to accommodate vast ranges of values.
    • The IEEE 754 standard is a common way to represent floating-point numbers in computers. The standard defines single-precision (32-bit) and double-precision (64-bit) formats.

    Other Binary Codes

    • Alphanumeric representation codes:

      • ASCII (American Standard Code for Information Interchange): 7-bit code, widely used
      • EBCDIC (Extended Binary Coded Decimal Interchange Code): 8-bit code, less common
      • Unicode: A wider character encoding system capable of dealing with a much bigger set of characters. 16 bits/character, designed to deal with multiple languages.
    • BCD (Binary Coded Decimal): Each decimal digit is represented by its binary equivalent, e.g. "0" as "0000", "1" as "0001. Four bits per digit.

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    Description

    Test your understanding of number systems and their conversions. This quiz covers key concepts including binary, decimal, octal, and hexadecimal systems, as well as methods for converting between them. Challenge yourself and reinforce your knowledge in computer science!

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