Decimal to Binary Conversion Video Lecture | Digital Electronics - Electrical Engineering (EE)

in this video we're gonna talk about how
to convert a decimal number into a
binary number so let's go ahead and
begin so how can we convert 75 into a
binary number it helps to be familiar
with the powers of 2 2 to the 0 power is
1
2 to the first power is 2 2 to the
second power is 4 2 to the third power
is 8 2 to the fourth power is 16 2 to
the fifth power is 32 2 to the sixth
power is 64 2 to the seventh power is
128
now we don't need to go further because
128 exceeds 75 so the highest number
that is the highest base 2 number that
is less than 75 is 64 so we're going to
start with 64 now in this video I'm
gonna show you two ways to convert a
decimal number into a binary number the
first half of the video will focus on
the subtraction method and the second
half will focus on successive division
so I'm going to show you both ways and
then you can pick and choose which
method you prefer now once you have your
first number which is 64 in this case
subtract let's subtract 275 by 64 and so
that will give us 11 now the highest
number that's under 11 is 8 16 exceeds
11 so we can't use that so let's put an
8 here and then let's subtract 11 by 8
11 minus 8 is 3 and so the next highest
number just under 3 is 2 and so let's
put a 2 here and then 3 minus 2 is 1 and
so the next highest number is a 1 and we
could stop here because if you add these
numbers 64 plus 8 that's 72 72 plus 2 is
74 74 plus one is 75
these four numbers add up to 75 now once
you have that you can begin to write the
numbers in binary so because we have a
64 we're gonna put a 1 we don't have a
32 so let's write a 0 we don't have a 16
we do have an 8 so let's put them on we
do not have a 4 so let's put a 0 but we
do have a 2 and a 1 so 75 is equal to 1
0 0 1 0 1 1 and so that's one simple way
in which you can convert a decimal
number into a binary number now here's
another example let's say if we have the
number 142 let's convert that into a
binary number so let's write the list of
numbers that we're gonna work with 128
64 32 16 8 4 2 and 1 so the highest
number under 142 the highest base-2
number is 128 so let's start with that
and then if we subtract 148 by I mean
142 by 128 that's gonna give us 14 and
so the next highest number just under 14
is 8 and so 14 minus 8 will give us 6
but let's put the 8 here now the next
highest number that's under 6 is 4 so if
we subtract 6 by 4 that will give us 2
so let's put the 4 here and then 2 minus
2 will give us 0 so we could stop at the
tune and so you can check it if you type
in 128 plus 8 plus 4 plus 2 that will
give you 142 so make sure that these
numbers add up to this number so you
want to find all the base 2 numbers that
add up to this number once you do that
and then you can convert it into a
binary number
so this is gonna be one we don't have a
64 nor do we have a 32 or 16 we do have
an 8 a 4 and a 2 and we don't have a 1
so 142 is basically 1 0 0 0 1 1 1 0 and
so that's how you can convert a decimal
number into a binary number now here's
another example let's try a bigger
number 339 go ahead and work on that
example so this time we need a number
that's higher than 128 128 times 2 is
256 so we're gonna start with 256 and
then 128 and then 64 32 16 8 4 2 & 1 so
256 is the highest number in its list
that's just under 339 and so let's
subtract 339 by 256 and so this will
give us 83 the next highest number the
highest base 2 number that's under 83 at
64 so let's subtract 83 by 64 and that
will give us 19 and let's not forget to
write the 64 here now the next highest
number under 19 is 16 so let's do 19
minus 16 and so that will give us 3 and
so let's write the 16 and then the next
highest number that's under 3 is 2 and
so 3 minus 2 is 1 so let's put the 2
here and then 1 minus 1 is 0 so we need
to include the 1 as well and then check
the work make sure that these numbers
all of these base 2 numbers add up to
339 and so type in 256 plus 64 plus 16
plus 2 plus 1 and that will give you 339
just to make sure that you did
everything correctly now let's write the
numbers so we have a 256 we do not have
a 128 we do have a 64 we do not have a
32 we have a 16 and since we don't have
a 8 or 4 we're gonna write a 0 we do
have a 2 latter one so we replaced that
with a run so 1 means on or yes and the
0 means off or no and so this is the
answer
so 339 is equal to 1 0 1 0 1 0 0 1 1 now
the second method involves successive
division and so let's go over the three
examples that we did used in the second
method so this allows us to confirm our
answer so in the first example we said
that 75 is equal to the binary number 1
0 0 1 0 1 1 let's confirm that using
successive division so here's what you
need to do start with 75 and divided by
2 75 divided by 2 is 37 point 5 so what
this means is that it's 37 remainder 1
now take the 37 and then divide that by
2 so 37 divided by 2 is 18 point five so
that's 18 remainder 1 then take the 18
divide that by 2 18 divided by 2 is
exactly nine with no remainder or
remainder 0 and then 9 divided by 2 is
4.5 so we say it's 4 remainder 1 and
then 4 divided by 2 is exactly 2 so it's
2 remainder 0 and then 2 divided by 2 is
1 exactly 1 so 1 remainder 0 and then
finally 1 divided by 2 that's basically
0.5 so we could say it's 0
remainder one and then we stop here so
at the bottom you have the MSB or the
most significant bit at the top you have
the LSB or the least significant bit now
the way you read it is from the most
significant bit to the least significant
bit so basically from the bottom to the
top so look at the numbers that we have
so we have a 1 a 0 and then the 0 1 0 1
1 which is basically the numbers that we
have there so if you write it from
bottom to top it's 1 0 0 1 0 1 1 so
hopefully you see that and so that's how
you can get the same answer using
successive division now let's go over
the second example
so let's say we have 142 you successive
division to convert it to a binary
number so let's divide this by 2 so 142
divided by 2 is exactly 71 so it's 71
with a remainder of zero and then 71
divided by 2 that's thirty five point
five so it's 35 remainder one and then
let's take 35 and divide that by two so
that's going to be 17.5 or 17 remainder
one and then 17 divided by two is eight
point five so that's eight remainder one
and then 8 divided by 2 is exactly 4 so
that's 4 remainder 0 and then 4 divided
by 2 is exactly 2 so 2 remainder 0 and
then 2 divided by 2 is exactly 1 so 1
remainder 0 and then finally the 1/2 is
point 5 so that's 0 remainder 1 so we're
going to read it from the most
significant bit to
least nificant bin so from the bottom to
the top so it's gonna be 1 0 0 0 1 1 1 0
which if you rewind the video you'll see
that we have this answer now let's work
on the last example 339 so let's divide
339 by 2 this will give us 169 point 5
or 169 and remainder 1 and then divide
169 by 2 and so that's gonna be 80 4.5
or 84 remainder 1 and then 80 4 divided
by 2 that's exactly 42
so 42 remain to 0 and then 42 divided by
2 is exactly 21 and then 21 divided by 2
that's ten point five so it's 10
remainder 1 and 10 divided by 2 is
exactly 5 so 5 remainder 0 5 divided by
2 is 2 point 5 so that's two amanda 1
and then 2 divided by 2 is exactly 1 and
1/2 is always point 5 so that's always
the V 0 remainder 1 so let's go from the
most to the least significant bit so
starting with the number on the bottom
it's gonna be 1 0 1 0 1 0 0 1 1 and so
this is 339 as a binary number and so
that's it for this video so now you know
how to convert decimal numbers into
binary numbers you have two ways of
doing it thanks for watching