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https:/.../emt011080p.mp4

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    Hello and welcome to the first
    video of the binary numbers. In
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    this video. I would like to
    introduce you to the binary
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    numbers and the binary number
    system, but for us to understand
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    that we need to look at what the
    decimal number system is and we
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    need to look at the powers
    because powers are at the heart
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    of every number systems. So
    let's start with the powers.
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    3 to the power of two is 3
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    * 3. And for example, 5
    to the power of four is 5
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    * 5 * 5 * 5. So
    there are two important concepts
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    in here, the power.
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    And the base, they both can be
    any different whole numbers.
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    So the power tells us how many
    times we need to multiply the
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    base together. So in this
    particular case, four tasmac 2
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    multiplied the base 5 by itself
    four times, and in the example
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    of three, the two tags need to
    multiply the three by itself
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    twice. Now there are two
    important powers that we need to
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    draw your attention to the first
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    one. Is any number to the zero
    power is by definition is always
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    one. For example.
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    7 to the power of 0 is 1
    two to the power of 0 is one
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    and 10 to the power of 0 is
    also one another important
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    power. Is any number raised
    to the first power is just the
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    number itself for example?
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    7 to the first power equals to
    7, two to the first power equals
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    to two and 10 to the first power
    is equal to 10.
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    By definition, the decimal
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    number system. Is a
    base 10 positional.
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    Number system.
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    Which uses 10 digits.
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    And these 10 digits are 012 all
    the way up to 9. So that's the 9
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    digits plus zero, which makes
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    them 10. Now what does it mean
    based on and positional the base
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    10 taskview that using 10 digits
    and every place value or every
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    position is represented by
    powers of 10 and it's a
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    positional number system because
    if you place digits at different
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    positions they represent
    different values. The former
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    mathematics is representing each
    of the place values tend to zero
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    10 to the one.
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    1:50 2:50 and so
    on now what they mean as
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    numbers? 10 to 0 as we said
    before, it's 110 to the one
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    Eastern tented it too, is 100
    and 2:50 is 1000.
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    It might seems a little bit
    overcomplicated when you think
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    about the decimal numbers, but
    it is already built into the way
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    that we read our numbers. For
    example, if you read out 573
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    just the way you say the number
    you talk about decimal place
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    values 573, so the hundred 500
    tells you that five is at the
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    hundreds place. The 70 tells you
    that 70s at the 10s place and
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    three tells you that three is at
    the units place. Now, what
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    happens if I use the same 3
    digits but in a slightly
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    different order? So what happens
    if I say 735?
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    Well, as I was reading out the
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    number. You probably notice that
    now is 7 at the hundreds place,
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    three is at the 10 space and
    five is at the units place. So
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    depending on which place value
    and placing or which position
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    and placing the digits, they
    will represent different values.
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    The five in the first number is
    105 in the second number is just
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    five units. The three in the
    first number is 3 units, but in
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    the second number.
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    E 310 switches 30 and the
    seven in the first number
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    is seven 10s, which is 70
    and in the second number
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    is 700 which is 700.
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    Now I would like to draw your
    attention to the rule of the
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    zeros because so far I just
    picked out any digits which is a
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    non 0 digit. But what happens if
    I have good zeros in my number?
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    For example? What's the
    difference between 1007?
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    Andseventeen well without having
    the zeros in the number I end
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    up with a very much smaller
    number, so the zeros are
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    so-called place value holders.
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    So today telling me that at this
    place value I'm not using any of
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    the place value by placing the
    zero. So in this case I'm using
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    seven of the units, not using
    any of the 10s an I'm not using
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    any of the hundreds and I'm
    using one of the thousands
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    without the zeros here. I'm just
    telling you that I'm using seven
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    or the ones and I'm using one of
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    the tents. You will agree with
    me that the two numbers are
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    very, very different, so every
    time I need to build up a bigger
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    number without using the in
    between place values, I always
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    had to place a 0 here.
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    Now we can build up a decimal
    place value table and the former
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    place value table would look
    like this. It's just basically
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    the heading you have got the
    powers and the equivalent
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    decimal values. Now how can you
    use a place value table like
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    this to position different
    numbers in that? Now we talked
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    about a few different numbers,
    so let's see what they look like
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    in the place where you table so.
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    573 you put a five in the
    hundreds, seven in the Times
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    Seven in the 10s, and three in
    the units column. If we talking
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    about 735, we mix up the order.
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    Of the digits 17. One of the
    10s. Seven of the units and 1007
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    one of the thousand. None of the
    hundreds. None of the 10s and
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    seven over the units.
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    One thing I'd like you to notice
    is when you look at the place
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    value table. If you're going
    from right to left, you can spot
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    that the numbers from place
    value to place while you get 10
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    times bigger, so the values
    themselves, the place where used
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    gets 10 times bigger.
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    Now if we reverse the order and
    we going from left to right, the
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    place values themselves get 10
    times smaller, so this is again
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    another important feature of the
    place values themselves, which
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    will help us to extend the place
    value table in a later video to
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    introduce smaller numbers.
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    Now we have got all the
    conceptual understanding that we
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    need to build up the binary
    numbers. Binary numbers are very
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    important for computer science
    because binary numbers are
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    basically the way to communicate
    to the computer. Remember that
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    the computer at a very basic
    level will type up small
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    electrical circuits, and you can
    either turn on electrical
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    circuits on or off, and in the
    different combinations of these
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    electric circuits you can tell
    the computer to do different
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    instructions. So depending on
    what kind of binary number
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    instructions you're giving to
    the computer, the computer will
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    carry out different calculations
    or different instructions.
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    By definition, the binary
    number system is base
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    two positional number system.
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    We using 2 digits.
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    And these two digits are
    zero and one.
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    So what does the place where you
    table look for the binary
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    numbers? But because it's a base
    two number system, every place
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    value is a power of two. So what
    are these powers?
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    2 to the power of 0 two to the
    power of 1 two to the power of 2
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    to the power of. 3 two to the
    power of four. 2 to the power of
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    5 and I can go on forever. As
    you see the differences now.
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    That instead of base 10, I'm
    just replacing the Terminator 2,
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    but the powers themselves stay
    the same. Now what does it mean
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    for the actual values? What is 2
    to the zero? While remember any
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    number to the Zero power is 1
    two to the one, any number to
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    the first power itself, so it's
    2 two to two 2 * 2 is 4, two to
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    three 2 * 2 * 2 is 8, two to
    four is 16 and two to five.
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    He's 32 and I can go
    on for higher values.
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    So when we look at the place
    values themselves compared to
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    the decimals, Now when I go from
    right to left, the place values
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    get doubled. So from one we can
    get to 2 from 2 began get to 4
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    from 4 we can get to 8, they
    double up and if I go from left
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    to right the opposite direction
    they get halved from 32 to 16 I
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    get by having it and from 16 to
    8 I get by having it again so.
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    This is a common feature of the
    place where you tables any
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    number system because there are
    other different number systems.
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    Every time when you go from
    right to left, the place values
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    get multiplied by the base.
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    And when you go from left to
    right, the place values get
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    divided by the base.
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    So when we look at the binary
    place value table, it's like the
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    numbers I showed you before, but
    put into a nicer format.
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    So what happens in the here in
    the decimal place value table?
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    We had quite a lot of different
    digits that we could play around
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    with. We had the digits from
    zero to 9, but what happens in
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    binary? Which 2 digits can we
    use here? Just the zero and one.
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    So. A binary number is
    nothing else but a string
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    of ones and zeros.
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    For example, this is a binary
    number. What it means then for
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    the place values is that with
    one I'm saying that use the
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    corresponding place value and
    with zero I'm saying don't use
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    the corresponding place value,
    so the placeholder property of
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    the zero becomes really
    important and comes up a lot
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    more often than in decimal
    numbers.
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    Let's look at a few more binary
    numbers. So basically I can just
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    use any ones and any zeros and
    place them in any order whatever
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    to build upon binary number. So
    let's say 1011001 it's a binary
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    number, 100001 is also binary
    number, or 1011. Again a binary
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    number. Now you probably notice
    that because we only using ones
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    and zeros. Every single one of
    them could also be a decimal
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    number. For example, the last
    one could be 1011 in decimal. So
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    how can we make a distinction
    between binary and decimal?
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    So there is a very common
    notation to distinguish between
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    binary and decimal numbers. So
    if you see a number which only
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    uses ones and zeros to make sure
    that this is a binary number,
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    you put a little two in
    subscript. And if you want to
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    indicate that this is a decimal
    number, you put a little
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    subscript of 10, indicating that
    this is a decimal number.
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    So if it's not clear enough from
    context, always look for the
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    subscript. It is a binary
    number. Or is it a decimal
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    number? Now it's very, very
    important that you are making
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    difference between the number
    itself and the notation of
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    signaling which system working
    in this letter notation, the
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    number 2 and here the number 10
    are not part of the number. As
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    long as the calculations go.
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    This is just a way of telling
    me or you or anybody ask that
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    this is a binary number. Once
    we are aware of that, this is
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    a binary number. This two
    becomes redundant, so as long
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    as the calculations go, you
    can leave this number.
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    So I hope that you have a
    better understanding of the
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    binary and the decimal number
    systems in the next few
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    videos. I will show you what
    we can do with the binary
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    numbers.
Title:
https:/.../emt011080p.mp4
Video Language:
English
Duration:
14:59

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