Data Representation using Signed Magnitude

00:05:58
https://www.youtube.com/watch?v=1k71RxUtgUY

Summary

TLDRThis lecture explores four methods for binary representation: unsigned magnitude, signed magnitude, ones complement, and two's complement. Unsigned magnitude only supports positive numbers, whereas the other methods allow both positive and negative. The focus is on the signed magnitude method, which uses an additional sign bit to indicate positive or negative numbers. The lecture includes examples of binary representation for numbers, explains the range of signed magnitude, and assigns homework for students to practice representing numbers using this method. The next lecture will delve into ones complement.

Takeaways

  • 🔢 Four ways to represent binary numbers: unsigned magnitude, signed magnitude, ones complement, and two's complement.
  • ➕ Unsigned magnitude can only represent positive binary numbers.
  • 🔄 Signed magnitude can represent both positive and negative binary numbers.
  • 👁️ Positive numbers are represented in the same way in all four methods.
  • ✖️ In unsigned magnitude, minus numbers cannot be represented.
  • ⚙️ Signed magnitude uses a sign bit; 0 for positive, 1 for negative.
  • 📝 Example: In signed magnitude, +6 is 0 110 and -6 is 1 110.
  • 🧮 Sign magnitude range for n-bit: -2^(n-1) to 2^(n-1) - 1.
  • 📚 Homework: Represent numbers using signed magnitude.
  • 💡 Next lecture will cover ones complement.

Timeline

  • 00:00:00 - 00:05:58

    This lecture covers binary numbers representation, focusing on four methods: unsigned magnitude, signed magnitude, one's complement, and two's complement. In unsigned magnitude, only positive binary numbers can be represented. Signed magnitude allows for both positive and negative numbers by adding a sign bit, where '0' indicates a positive number and '1' indicates a negative number. Positive numbers are represented the same way in all four systems, so emphasis will be on negative numbers. The lecture focuses on unsigned and signed magnitude representations, with detailed examples provided for each. Lastly, the range for signed magnitude is explained, followed by homework problems for practice.

Mind Map

Video Q&A

  • What are the four ways to represent binary numbers?

    The four ways are unsigned magnitude, signed magnitude, ones complement, and two's complement.

  • Can negative numbers be represented in unsigned magnitude?

    No, unsigned magnitude can only represent positive numbers.

  • How is the sign bit used in signed magnitude representation?

    In signed magnitude, a sign bit of 0 indicates a positive number, while a sign bit of 1 indicates a negative number.

  • Is the representation of positive numbers the same in all four methods?

    Yes, positive numbers are represented in the same way across all four methods.

  • What is the range of numbers in n-bit signed magnitude representation?

    The range is from -2^(n-1) to 2^(n-1) - 1.

  • What homework problems are given in this lecture?

    The homework involves representing +5 and -5, +9 and -9, and +16 and -16 using signed magnitude representation.

  • What will be covered in the next lecture?

    The next lecture will cover ones complement.

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  • 00:00:04
    in this lecture we will learn binary
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    numbers representation there are four
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    ways first one is unsigned magnitude
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    second one is signed magnitude third one
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    is ones complement and last one is two's
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    complement in case of unsigned magnitude
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    we can represent only positive binary
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    numbers let me write this down we can
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    represent only positive
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    binary numbers and in case of sign
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    magnitude we can represent both positive
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    both positive and negative binary
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    numbers in case of ones complement
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    representation we can represent positive
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    and negative binary numbers and in case
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    of two's complement representation again
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    we can represent positive and negative
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    binary numbers so in unsigned we can
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    only represent positive and in case of
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    signed ones complement and two's
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    complement we can represent both
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    positive and negative binary numbers in
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    all four representations positive number
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    is represented in same way I will write
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    this down
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    in all four representations
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    positive
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    number is represented in
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    same way this is very important point
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    and thus we have to focus only on
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    negative number representation in this
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    lecture we will focus on unsigned and
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    signed magnitude representation and in
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    the next lecture we will study ones
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    complement so let's start with unsigned
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    magnitude representation
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    if I want to represent plus six
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    then it will be represented as 1 1 0 and
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    if I want to represent minus 6 then we
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    can't
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    represent minus 6 because in case of
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    unsigned magnitude representation we can
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    only represent positive binary numbers
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    now we will move to signed magnitude
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    the most important part of this present
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    in case of sign-magnitude we can
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    definitely represent positive and
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    negative binary numbers and if I want to
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    represent positive of six then first I
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    will represent the magnitude the
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    magnitude is 1 1 0 this is the
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    representation of 6 and now I have to
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    add one extra bit 0 and this extra bit
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    is called as sign bit and if this sign
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    bit is 0 the number is positive and if
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    this sign bit is 1 the number is
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    negative for example if I want to
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    represent minus 6 then again I will
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    represent the magnitude first 1 1 0 and
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    then I will add one as MSB so this 0 & 1
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    are
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    sign
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    bit and they are MSB of the number right
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    this is MSB the rightmost bit of the
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    number and 1 1 0 is the
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    magnitude so in case of sign-magnitude
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    representation we have two parts first
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    one is the sign bit which decides
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    whether the number is positive or
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    negative and the second part is the
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    magnitude of the number so let me write
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    this down if sign bit sign bit is 0 this
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    implies
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    number is positive and if sign bit is 1
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    this implies number is negative so this
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    is important
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    we will see one more example
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    let's represent plus of 13 so this 13 I
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    will represent first it is 1 1 0 1 the
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    magnitude and for this plus I will add 0
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    so positive of 13 in case of
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    sign-magnitude representation is
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    represented by 0 1 1 0 1 and if I want
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    to represent minus 1/2 13 then again I
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    will do the same thing I will represent
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    13 first the magnitude part and then
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    this minus will add 1 here so minus 13
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    is 1 1 1 zero-one in case of
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    sign-magnitude i hope this is clear to
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    you now we will move to next part of
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    this presentation that is range of
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    signed magnitude the range of sign
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    magnitude is from minus of 2 raised to
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    power n minus 1 minus 1/2 plus of 2
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    raised to power n minus 1 minus 1 so
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    this is the range for sign magnitude
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    where n where n is the number of
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    variables and for 4 variables n is equal
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    to 4 so we have minus of 2 raised to
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    power 3 minus 1 4 minus 1 is 3/2
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    plus of 2 raised to power 3 minus 1 2
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    raised to power 3 is 8 8 minus 1 is 7 so
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    minus 7 2 plus 7 is the range of sign
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    magnitude for 4 variables now we will
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    move to homework problems I have three
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    homework problems for you in first
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    homework problem you have to represent
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    plus 5 and
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    minus 5 in second homework problem you
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    have to represent plus 9 and minus 9 in
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    third and last homework problem you have
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    to represent plus 16 and
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    minus 16 and for representation
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    use signed
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    magnitude representation okay so this is
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    all for this presentation see you in the
  • 00:05:57
    next one
Tags
  • Binary Numbers
  • Unsigned Magnitude
  • Signed Magnitude
  • Positive and Negative
  • Sign Bit
  • Range
  • Homework
  • Next Lecture