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

in this lesson we're going to talk about
how to convert a decimal number into an
octal number so let's start with this
example 394 which is in the base 10
system how can we convert it into an
octal number which is in the base 8
system well the first thing you need to
do is take the number that you have and
divide it by 8 so let's use a calculator
to do that now 394 divided by eight is
forty nine point two five now what we
need to do here is we need to identify
the remainder so we have 49 and then
remainder in order to identify it take
the decimal value then the numbers after
the decimal point that is 0.25 and then
multiply it by eight so eight times 0.25
is 2 so we have 49 remainder 2
now take the 49 and then divide that by
eight 49 divided by eight is six point
one two five so this is going to be six
remainder and then multiply 0.125
by 8 so 8 times 0.125
is one so we have six remainder 1 next
take six and divided by eight now
because six is less than eight we could
say that 8 goes into six zero times with
a remainder of 6 if you take six divided
by eight it's going to give you zero
point seven five so this number gets
transferred here and then if you
multiply the point seven five by eight
it's going to give you six and so you
get a remainder of 6 now the way you
read your answer is you read it starting
from the most significant digit
to the least significant digit so you
read the remainders from the bottom to
the top so the first number is a six and
then after that we have a 1 and then we
have a 2 and this is in the base 8
system so 394 in the base 10 system is
equal to 6 12 and a base 8 system and so
that is how we can convert a decimal
number into an octal number now let's
work on another example so try this one
784 go ahead and use a calculator to
convert it into an octal number so what
we're going to do is we're going to take
784 and divided by 8 784 divided by 8 is
exactly 98 so this is 98 remainder is 0
now let's take a 98 and divide it by 8
so you should get 12 0.25 so this is 12
remainder and then 0.25 times 8 is 2 so
it's 12 remainder 2 next let's take this
12 and then divide it by 8 so 12 divided
by 8 is 1.5 so this is 1 remainder and
then 8 times 0.5 is 4 so it's 1
remainder 4 now our next number is 1 so
1/8 so because 1 is less than 8 we can
say that 8 goes into 1 0 times with a
remainder of whatever this is in this
case the remainder is 1 and now we're
going to read it from the bottom to the
top so we have a 1 a 4 a 2 and a 0 so
therefore 784 as a decimal
is basically 14:20 in the octave system
so this is the answer now let's try one
more example using a calculator so let's
try 64 base 10
let's converted to an octal number so
feel free to pause the video and try
that example problem so we know the
process by now the first thing to do is
to divide it by 8 12 64 divided by 8 is
exactly 158 and so we say this is 158
remainder 0
now let's taking on 58 and divided by 8
and so we're gonna get nineteen point
seven five and so this is going to be 19
remainder now if we multiply eight five
point seven five that's going to give us
six so we have 19 remainder six now
let's take the 19 and divide it by 8 19
divided by eight is two point three
seven five so this is 2 remainder and
then 0.375 times eight
extreme so we have two remainder three
now let's take the two and divide it by
8 so 2 is less than 8
therefore eight goes into two zero times
with a remainder of 2 so now let's read
it this way so it's two three six zero
base 8 so this is our answer in the octo
system now let's talk about how to
convert a decimal number into an octal
number but without using a calculator
because sometimes you might be given a
test question and you can't use a
scientific device so let's talk about
how to do that okay let's fix that
so let's convert 62 into an octal number
so we need to divide 62 divided by 8 so
let's use long division how many times
this 8 go into 62 8 goes into 60 to 70
times 8 times 7 is 56 and 62-56 is 6 so
this is our remainder
so 62 divided by 8 is 7 remainder 6 and
so that's how we can do it next we have
7 divided by 8 since 7 is less than 8 we
could say 8 goes into 7 zero times with
a remainder of 7 and so reading it this
way we could see that it's 7 6 476 in
the octo system so this here is a final
answer for this problem and so as you
can see converting it from a decimal
number into an octal number it's pretty
straightforward you simply needs to
divide by eight Collector remainders and
then you'll get your answer let's do
another example without the use of a
calculator let's use 468 so go ahead and
try this problem so let's divide 468 by
8 so let's start with long division how
many times does 8 go into 46 8 times 5
is 40 8 times 6 is 48 - that's too much
so we could say that 8 goes into 46 5
times 8 times 5 is 40 46 minus 40 is 6
now let's bring down the 8 so how many
times is this 8 go into 68 8 goes into
60 8 8 times 8 times 8 is 64 with a
remainder of 4 because 4 is less than 8
so the first answer is 58 remainder 4
now let's take 58 and let's divide it by
8 so let's use long division now 8 goes
into 58 7 times 8 times 7 is 56 and 58
minus 56 is 2 & 2 doesn't go into 8 so
this will give us 7 remainder 2 now the
last thing we need to do is take this
number and divided by 8 so 8 doesn't go
into 7 it goes into 7 zero times with a
remainder of what we see here are 7 and
so we're gonna read it from the bottom
to the top and that's going to give us
our answer so 468 and the base 10 system
is equal to 7 - 4 in the base 8 system
and so that is how we can convert a
decimal number into an octal number
without the use of a calculator