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Conversion from Binary to Decimal | Darwin Ong | YouTubeToText
YouTube Transcript: Conversion from Binary to Decimal
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topic
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but updates on my lectures
for the conversion conversion from
system is the internal language
of electronic computers
so these are the steps
how to use positional notation so we
have one zero zero one one
and i may be sign two so first write
down the binary number and list the power
power
of two from left to right
so let's say we we want to convert the
binary numbers
one zero zero one one zero one one base
of two to decimal
first write it down then write down the
powers of 2 from right to left
so i start at 2 raise to 0 degrees
no raise to 0 not zero degrees raised to zero
zero
i'm reading it as one so increment
the exponent by one from each
power so it stops
stop when the amount of elements in
list is equal to the amount of digits in the
the
binary numbers or number i mean
so the example number one zero zero one one
one
zero one one has eight digits so the list
list
with eight elements would like look like this
this
one twenty eight three sixty four thirty
two six one
sixteen eight four two one four
two one so panopoulo remember [Music]
to the 6 is 64 2 to the p 32 to the
fourth 16
to the three is eight to the square root is
is
four to the one is two and two three
zero is one so yeah okay next step
write the digits of the verani number
below the the corresponding
powers of two you can get another
argument so
now just write one zero zero one one
zero one one below the
numbers so 1 28 64 32 16
8 4 and 2 and 1 so that
each binary digit corresponds with each
power of two
so the one to the right of the binary
number should
correspond with the one on the right of
the listed
powers of two and so on so you can
also write the binary digits above the
powers of two
if you prefer it that way so what is
important is that
they match up you know important
okay so for example one
zero zero one one zero one one okay
so next connect the digits in the binary
number with their corresponding powers
of two
so draw a line starting from the right
connecting each consecutive digit
of the binary number to the power of
two that is next is the least above its
begin by drawing a line from the first
digit of the binary number
to the first power of two in the fourth list
list
above it then draw a line from the
second digit of the binary number
to the second power of two in the fleece
continue connecting each digit with each
corresponding power of two this will
help you
visually see the relationship between
the two sets of
step four write down the final value of each
each
power of two so move through each digit
of the binary number if the digit is
a one write its corresponding power of
two below the line
under the line of the digit if the digit
is a zero right zero below the line
under the digit
so since one corresponds with one it becomes
becomes
a one since two corresponds with one it
becomes two
since four corresponds with zero it
becomes zero shameful any number that
multiplies zero is zero
so since a is corresponds with one it
becomes eight
since 16 corresponds with one it becomes
16 so 32 corresponds to zero it becomes zero
zero
and 64 corresponds with zero and
therefore becomes zero
while 128 corresponds with one so n
becomes one weight one way i'm getting
so remember 128 times 1 is
128. 64 times 0 is
0 32 times 0 is 0. 16 times
1 is 16 8 times 1 is 8
four times zero is zero two times one is two
two
and then one times one is one so it
takes a good
next step five add the final value so
now the
add the like the number written below
the line so here was
it to do is 128 plus 0 plus 0 plus 16 plus
plus
8 plus 0 plus 2 plus 1 is equal to 155
so this is the decimal equivalent of the
little binary number is not it
so write the answer along with b
subscript so now all
you have to do is write 150 by 10
for the decimal procedure so show that
they are working with the decimal answer
so which must be operating in powers of
10. so the more you get
used to converting from binary to
decimal the more easy
it will be you for you to memorize the
power of two
so and you'll be able to complete the
tasks more quickly
anybody remember for here yeah i think
final answer nothing
so what are 55 bits of that in subscript yeah
for example use this method to convert a
binary number
with a decimal point to decimal form
so we have 1.1 base of two so you can
use this method
when you want to convert a binary number
such as 1.2
no what one point one base of two
decimals so all you have to do is
know the number on the left side of the decimal
decimal
is in in the units position like normal
while the number of the right side of
the decimal is in the
half's position for example one times
one half percent
diva so at the end so
the one to the left of the decimal point
is equal to 2
raised to 0 or 1 because
any number that 3 is 0 is 1. so the 1 to the
the
right of the decimal is equal to 2
raised to negative 1 which is 0.5
and add up one and five
and you'll get 1.5 which is equivalent
to 1.1
in decimal notation so i'm going to n
so 1.1 so
2 is zero and so this one
super canon attend one
zero is one plus
and 2 raised to negative 1 times 1 is 0.5
0.5
so we have again at that end we have 1.5
base of 10 because of the procedure nothing
nothing
so first write down the binary numbers
so this method does not use powers as such
such
it is simpler for converting a large
number in your
head because you only need to keep track
of a subtotal
so the first thing you need to do is to
write down the binary number
you'll be converting using a doubling method
method
let's say that the number you're working
is one zero one one
zero zero one we have base two
and subscript now write down okay so
second step starting from the left
double your previous total and at the
current digit so since you're working
with the binary number one zero one one zero
zero
zero one base of two your first digit
all the way on the left is one so your
previous total is zero
so since you haven't started yet you'll
have to double the previous total
zero and add one so the current digit is zero
zero
times two plus one is equal to one so your
your
so next step so double your current
total and at
the next leftmost digit so your current
total is one now
and the new current digit is zero so double
double
one and adds
zero so one times two plus zero is equal to
to
so repeat the previous steps just keep
going next double your current total and
add one
your next uh your next digit so two
times two plus one is equal to five your
current total
so we have 11 so your new total is 11
double your current 11 and then add zero
so equals
so we have equals to 22
and 22. so next step
repeat double your current total and add
zero so we have 44
plus or times two double dot attend plus
and zero another zero it's equal to 44.
next step so continue doubling your
current and
total and adding the next digit until
you run out of the
dates so now you're down to
your last number and are almost done so
all you have to do is take your current
total with 44 and double it
along adding one so the last digit which
is what
44 times 2 plus 1 is equal to 89 you're
all done so you
convert it 1 0 0 1 0 1 1 0 0 1
base of 2 to decimal notation to its
which is equal to 89
so okay so you're
write your final answer we have to show
that you are
working with a decimal so which has a base
base
of 10. so you finally answering more
okay next i'll use this method to convert
convert
it from any base to decimal so for example
example
doubling is used because the given
number is base of two
if the given number is it of different
base replace the two
indeed method with the base of the given
number for example we
if the given number is in the base of 37
so you you replace the the times 2
with times 37 so the final result will be
be
in decimal so we have the base of 10 for example
example
times 37 plus
1 which is equal to one because it
zero times thirty seven is zero so plus
one is equal to
so one times thirty seven plus
two so we have 39.
times 37 plus
39 37 plus 3 is 1 46
so this will be your final answer with
base of
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