Representation of Numbers and Fixed Point Systems
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Representation of Numbers and Fixed Point Systems

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Questions and Answers

What is the result of adding -46 and -25 using signed magnitude binary arithmetic?

  • -71 (correct)
  • 25
  • -25
  • 71

    • What is a key disadvantage of signed magnitude representation in computer systems?

  • It adds complexity to arithmetic operations. (correct)
  • It can only represent positive values.
  • It simplifies hardware implementation.
  • It allows only one representation for zero.

    • In one’s complement representation, how is negative 3 expressed in 8-bit binary?

  • 11111100 (correct)
  • 00000011
  • 11111101
  • 00000000

    • What is the effect of the carry bit in one’s complement addition?

    <p>It is added to the sum.</p> Signup and view all the answers

    In signing magnitude binary arithmetic, what happens when the signs of two numbers differ?

    <p>You take the absolute difference and apply the sign of the larger number.</p> Signup and view all the answers

    Why do computer systems prefer complement systems over signed magnitude representation?

    <p>They eliminate the need for subtraction.</p> Signup and view all the answers

    What is a result of using one’s complement representation regarding zero?

    <p>It allows negative zero and positive zero.</p> Signup and view all the answers

    When adding the values 48 and -19 in one’s complement, how is -19 represented?

    <p>11101100</p> Signup and view all the answers

    What is the result of converting the octal number (736.4) to decimal?

    <p>(478.5)10</p> Signup and view all the answers

    In binary, what is the decimal equivalent of the number (110.111)?

    <p>(6.785)10</p> Signup and view all the answers

    What is the correct method for converting a decimal fraction to a base R number?

    <p>Successive multiplications by R and accumulation of integer digits.</p> Signup and view all the answers

    Which of the following represents the hexadecimal number for decimal 13?

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

    When converting from binary to decimal, what does the binary digit in the 1's place represent?

    <p>It represents $2^0$.</p> Signup and view all the answers

    What is the base-2 (binary) representation of the decimal number 10?

    <p>1010</p> Signup and view all the answers

    Which numeral system uses the base value of 16?

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

    In converting the decimal number 54 to binary, which of the following is one of the steps involved?

    <p>Divide 54 by 2 and keep track of the quotients.</p> Signup and view all the answers

    How do you represent a positive number in two’s complement?

    <p>Convert it directly to binary.</p> Signup and view all the answers

    What is the resulting two’s complement representation of -3 in 8 bits?

    <p>11111101</p> Signup and view all the answers

    What indicates an overflow condition in signed two’s complement arithmetic?

    <p>When the carry in and carry out of the sign bit differ.</p> Signup and view all the answers

    In two’s complement arithmetic, how are binary numbers added?

    <p>By discarding any carries from the high order bit.</p> Signup and view all the answers

    What is the two’s complement representation of -19 in 8 bits?

    <p>11101101</p> Signup and view all the answers

    What happens when an overflow occurs in signed number representation?

    <p>The carry flag is set instead of the overflow flag.</p> Signup and view all the answers

    Which of the following statements about carry and overflow is true?

    <p>Carry and overflow can occur independently.</p> Signup and view all the answers

    What should be done to find the one’s complement of a binary number?

    <p>Invert all bits of the number.</p> Signup and view all the answers

    What is the primary operation involved in arithmetic subtraction using 2's complement?

    <p>Take the complement of the subtrahend and add it to the minuend.</p> Signup and view all the answers

    In floating point representation, what does the exponent signify?

    <p>The position of the radix point.</p> Signup and view all the answers

    Which of the following statements about signed integer representation is correct?

    <p>The sign bit is combined with the magnitude bits.</p> Signup and view all the answers

    When performing binary addition, what does the rule '1 + 1 = 10' indicate?

    <p>A carry of 1 is produced.</p> Signup and view all the answers

    What is the significance of the mantissa in floating point representation?

    <p>It is a signed fixed point number.</p> Signup and view all the answers

    How is the sum of two numbers calculated using signed magnitude binary arithmetic?

    <p>Separate the sign and magnitude and add as in decimal.</p> Signup and view all the answers

    Which of the following is NOT part of the binary addition rules?

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

    What is the outcome of the operation (±A) - B in 2's complement?

    <p>Add A and the complement of B.</p> Signup and view all the answers

    What component of a floating point number representation directly follows the sign bit?

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

    Which of the following statements is true regarding the representation of zero in floating point numbers?

    <p>Mantissa is 0 and exponent is the smallest representable number</p> Signup and view all the answers

    What is the main reason for using internal representation in computing?

    <p>For calculation efficiency</p> Signup and view all the answers

    What does the most significant position of the mantissa represent in floating point numbers?

    <p>A non-zero digit</p> Signup and view all the answers

    How are external representations of numbers converted for presentability?

    <p>Through Internal Representation</p> Signup and view all the answers

    What is the purpose of a unified floating point number representation in a computer?

    <p>To handle calculations more efficiently</p> Signup and view all the answers

    What distinguishes external representation from internal representation in computing?

    <p>External representation is for presentability.</p> Signup and view all the answers

    In the binary coded decimal (BCD) system, how is the decimal number 5 represented?

    <p>0101</p> Signup and view all the answers

    In a 16-bit floating point number representation, how many bits are allocated to the exponent?

    <p>6 bits</p> Signup and view all the answers

    What is implied in a floating point number representation regarding the radix point?

    <p>Its position is implied but not stored.</p> Signup and view all the answers

    Study Notes

    Representation of Numbers

    • Positional Number System: Represents numbers using a base (radix) and place value.
    • Common Bases: Decimal (R=10), Binary (R=2), Octal (R=8), Hexadecimal (R=16)
    • Decimal, Binary, Octal, Hexadecimal: Represent numbers using different bases with corresponding symbols.
    • Conversion between Bases:
      • Base R to Decimal: V(A) = S ak Rk, where A is the number, ak is the digit at position k, and R is the base.
      • Decimal to Base R:
        • Integer Part: Successive divisions by R, collecting remainders.
        • Fractional Part: Successive multiplications by R, collecting integer parts.

    Fixed Point Representations

    • Arithmetic Subtraction in 2’s complement: Compute (A) - (B) as (A) + (-B), where (-B) is the two’s complement of B.

    Floating Point Representation

    • Floating Point Number: Represents numbers with a mantissa (signed fixed-point) and an exponent.
    • Value Representation: V(F) = V(M) * RV(E), where F is the floating-point number, M is the mantissa, E is the exponent, and R is the radix.

    Signed Integer Representation

    • Binary Addition: Simple rules for adding binary numbers.
    • Signed Magnitude: Represents numbers with a sign bit and a magnitude.
      • Disadvantage: Two representations for zero (positive and negative).
    • One's Complement: Represents negative numbers by inverting all bits of the positive counterpart.
      • Disadvantage: Two representations for zero.
    • Two's Complement: Represents negative numbers by inverting all bits and adding 1 to the one's complement.
      • Advantage: Single representation for zero.
    • Detecting Overflow: In two's complement, overflow occurs when the carry-in and carry-out of the sign bit differ.

    External Representations

    • Internal Representation: Efficient representation for internal calculations.
    • External Representation: Human-readable representation for output.
    • BCD (Binary Coded Decimal): Represents decimal digits using 4-bit binary codes.

    Internal vs. External Representation

    • Numbers: Often require internal representation for efficiency and external representation for presentability.
    • Alphabets, Symbols, Numbers: Often do not require internal representation as they are not directly involved in calculations.

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    Description

    This quiz explores the different systems of representing numbers, including positional number systems like decimal, binary, octal, and hexadecimal. It also covers conversion methods between these bases and introduces fixed-point representations and floating-point numbers. Test your understanding of these fundamental concepts in computer science!

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