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

in this video we're going to talk about
how to convert a decimal number to a
hexadecimal number so how can we do this
well first you need to understand that
the decimal number is based on a base 10
system for example let's say if we have
the digit 49 the first digit can be
anything from 0 to 9 0 1 2 3 4 5 6 7 8 9
and the same is true for the second
digit we have 10 options to choose from
so the decimal system is a base 10
numbering system now what about the
hexadecimal system notice that it's
composed of two words hexa and decimal
hexa corresponds to six decimal as we
could see here corresponds to 10 and so
if we add 6 and 10 this will give us 16
so the hexadecimal memory system is a
base 16 system now you need to know the
numbers that corresponds from the
corresponds to the hexadecimal system
from the decimal system so the number
one in the decimal system has the same
value in the hexadecimal system so one
corresponds to one two corresponds to
two and three corresponds to three and
so forth five corresponds to five six
corresponds to six I'm gonna continue
the pattern here and I forgot one number
in that zero zero corresponds to zero I
started with one but we should have
started with zero now once you get to
ten that's where changes ten doesn't
correspond to ten ten in the decimal
system corresponds to a in the
hexadecimal system eleven in a decimal
system corresponds to B twelve
corresponds to C 13 corresponds to D and
then fourteen corresponds to e
fifteen corresponds to F and you stop at
fifteen because when you include zero
going up to fifteen
that's sixteen numbers and so the
hexadecimal system is based on sixteen
different numbers and letters now what
we're going to do is we're going to talk
about how to convert a decimal number to
a hexadecimal number using a calculator
because you can easily do it with a
calculator very fast and also just in
case you get a test where it says do
this problem no calculator and if you
get that we need to know how to do it
without a calculator so make sure you
understand the basics of long division
if you don't I recommend watching the
video I created on long division it's on
YouTube so if we type in long division
organic chemistry tutor it should come
up but let's begin let's start with 479
so how can we convert 479 which is a
base-10 number that's a decimal number
into a hexadecimal number how can we do
this the first step is to take 479 and
divide it by 16 so we said we're going
to use a calculator for this so let's go
ahead and do that
479 divided by 16 is twenty nine point
nine three seven five so here we have an
integer of twenty nine and then we need
to find a remainder to find a remainder
multiply 16 by 0.9 375 so 16 times point
nine three seven five that will give you
a remainder of fifteen then you start
with this number twenty nine and divide
that by 16 so let's move on to the next
row so it's 29 divided by sixteen that's
equal to one point eight one two five so
that's one remainder and to find the
remainder and multiply sixteen by twenty
eight one two five
and so that will give you a remainder 13
and then you need to take the run divide
that by 16 now we really don't need to
do the division here because one does it
go into 16 I mean 16 is going to 1 so we
could say it's 0 remainder 1 but if you
did it let's say if you taken 1 when you
divided by 16 are you gonna get point 0
6 to 5
so looking at this number you'll see
that we need to put a 0 here and then if
you multiply 16 by point zero six to
five you'll get 1 but you really don't
need to do the division you can see that
16 goes into 1 0 times with a remainder
now once you get a 0 this is when you
stop so focus on these numbers 1 13 and
15 I'm gonna rewrite it but let me get
rid of this stuff first so we had 1 13
and 15
so the remainders you want to convert
them to hexadecimal numbers 1 as a
decimal is 1 as a hexadecimal and based
on the chart that we wrote earlier 13
corresponds to D and 15 corresponds to F
now 1 is the most significant digit and
F is the least significant digit so we
need to write it in this order from the
most to the least significant digit
so therefore 479 in the base 10 system
as a decimal is 1 DF as a hexadecimal so
we can write a subscript of 16 to
indicate that this is a hexadecimal
number and so that's how you can convert
a decimal number to a hexadecimal number
using a calculator now let's try another
example 894 feel free to pause the video
use a calculator to convert the decimal
number into a hexadecimal number so
let's start with 894
and let's divide it by 16 894 divided by
16 is fifty five point eight seventy
five so that's gonna be fifty five
remainder and take eight point seven
five and multiply it by sixteen and so
that's going to give you a remainder of
fourteen now let's use this number 55 or
you could say this number that we have
here and let's divide that by 1650 5/16
that's three point four 375 and so we
have three remainder and then take point
for three seventy-five multiply that by
sixteen and that will give you a
remainder seven now let's take three
3/16
that's gonna give us a number less than
one so we can go straight to the answer
that's going to be 16 goes into three
zero times and with three remaining if
you do three over sixteen you'll get
0.1875 and so here you have a zero and
then 0.1875 is going to be three so
that's a remainder of 3 if you do 0.1875
times 16 that will give you three now
let's convert the remainder values to
hexadecimal values so 3 as a decimal is
three in the hexadecimal system seven is
still seven now fourteen corresponds to
a letter so using a chart fourteen
corresponds to e so we're gonna write it
from the most significant digit to the
least significant digit
thus 894 is three 7e
in the hexadecimal system and so that's
it for this example
now let's try an example with out a
calculator let's use a bigger number 32
84 so convert this decimal number into a
hexadecimal number so if we're going to
do this without a calculator we need to
do long division how many times the six
can go into 32 16 goes into 32 2 times
16 times 2 is 32 so we get a remainder
of 0
and so we need to bring down to 8 now
how many times does 16 go into 8 16 goes
into 8 zero times 16 times zero is zero
and so we still get a difference of
eight so now we need to bring down to
four how many times does 16 go into 84
16 goes into 84 5 times 16 times 5 is 80
and so we get a remainder of 4 so it's
going to be 205 remainder 4 so then we
write this 32 84 divided by 16 is 205
remainder 4 so now we need to divide 205
by 16 so let's use long division
let me do it over here how many times
does 16 go into 2016 goes into 20 one
time 16 times 1 is 16 20 minus 16 is 4
and then we'll need to bring down the 5
now how many times does 16 go into 45 16
times 2 is 32 but 16 times 3 is 48 which
is too high so it goes into it two times
and then 45 minus 32 is 13 so 205
divided by 16 is 12 remainder 13
now for the last one we need to divide
12 by 16 so 16 doesn't go into 12 it
goes into 12 zero times with a remainder
of 12 so now let's focus on these
numbers let's convert them to
hexadecimal values so 12 and the decimal
system corresponds to C in the
hexadecimal system 13 corresponds to D
and 4 corresponds to 4 so we're gonna
read it this way starting with C so it's
gonna be C d-four base 16 and so that's
how you can convert a decimal number to
a hexadecimal number using a calculator
actually I meant to say without using a
calculator so let's do another example
like that 7950 6 so convert this base 10
number into a hexadecimal number so
let's begin by taking 79 56 and less
divided by 16 so let's use long division
now it's good to understand your 16
times tables if not keep adding 16 16
plus 16 is 32 32 plus 16 is 48 48 plus
16 is 64 64 plus 16 is 80 and then 96
and then you could add some more if you
need to so how many times does 16 go
into 79 the highest number in just under
79 is 64 so 16 goes into 79 4 times 16
times 4 is 64 now 79 minus 64 is 15 and
so we need to bring down to 5 in this
case we need some more numbers 96 plus
16 is 1 12 and 112 plus 16 is 128 1
28 plus 16 is 144 and then the next one
is 160 when making a list like this you
never need to go past 10 now 16 goes
into 155 9 times 16 times 9 is 144 and
155 minus 144 is 11 now let's bring down
to 6 16 goes into 116 7 times 16 times 7
is 112 with a remainder of 4 so we could
say that 7950 6 divided by 16 is 497
remainder 4
now you may want to write this
information down just in case I need to
erase it to make more room so now let's
divide 497 by 16 so how many times does
16 go into 49 16 goes into 49 3 times 16
times 3 is 48 49 minus 48 is 1 and then
let's bring down the 7 16 goes into 17
one time with a remainder of 1 so now I
need to erase this so 497 divided by 16
is equal to 31 remainder 1 so now let's
divide 31 by 16 so this we can do in our
heads 16 goes into 31 one time and a
remainder is the difference between 31
and 16 which will be 15 so now let's
convert these into hexadecimal values so
15 corresponds to F and then actually no
we're not finished yet this needs to be
a zero so now we need to divide one by
16 1 divided by 16 is 0 with a remainder
of 1 so now we're finished so don't
forget that because I almost did and you
need to get a zero here before you could
finish so a remainder of 1 1 corresponds
to 1 15 corresponds to F the 1
corresponds to 1 and 4 corresponds
that's 4 so writing it from the most
significant digit so the least
significant digit it's going to be 1 F 1
for base 16 and so this is the answer
now let's do one more example but this
time we're gonna do it both ways and
let's use a bigger number fourteen
thousand two hundred and fifty nine so
let's convert this base-10 number into a
base sixteen number go ahead and try it
so first let's use a calculator fourteen
thousand two hundred fifty nine divided
by sixteen and so that's going to be 891
point one eight seven five which I'm
going to write that number here just to
conserve space so it's eight ninety one
remainder and then take the decimal
number multiply it by 16 so 0.1875 times
sixteen that will give us a remainder of
3 now let's take 891 and let's divide
that by 16 and so that's going to be
fifty five point six eight seven five so
that's fifty-five remainder and then
take point six eight seven five multiply
that by sixteen so that will give us
remainder eleven and then it's going to
be 55 divided by sixteen which is three
point four three seven five so we're
going to get 3 and then point four three
seven five times 16 is seven next 3
divided by sixteen sixteen does it go
into three so 16 goes into three zero
times with a remainder of 3 and that's
where we stop now let's get rid of this
and let's convert the remainder values
into hexadecimal values so 3 corresponds
to three seven corresponds to seven
eleven corresponds to B and three
corresponds to three so
writing it from bottom to top it's gonna
be three 7b three base 16 and so that's
how you can do it using a calculator now
let's do it without using the calculator
so we need to take 14,000 259 and
divided by 16 so let's do long division
now if you wrote that list that we had
earlier you'll know how many times 16
goes into 142 16 does it go into 14 so
we have to use 142 now I'm going to
rewrite the list we only need it up to 9
so this is one two three four five six
seven eight nine
so 16 goes into 142 eight times 128 is
the highest number just under one forty
two so 16 times eight is 128 and 142
minus 128
that's 14 now 16 goes into 145 nine
times 16 times 9 is 144 and so we have a
difference of 1 16 goes into 19 one time
and so we get a remainder of 3 so this
becomes 8 9 1 remainder 3 so now let's
take 891 and let's divide that by 16 16
goes into 80 9 5 times 16 times 5 is 80
the difference is 9 16 goes into 91 5
times as well and so here the
differences 11 16 doesn't go into 11 so
vast a remainder this gives us 55 the
remainder 11 now let's divide 55 by 16
16 goes into 55 3 times 16 times 3 is 48
and a remainder is 7 so we have 55
divided by 16 which is 3 remainder 7
and then we need to divide 3 by 16 which
16 goes into 3-0 times with 3 remaining
now let's convert the remainder values
to hexadecimal so 3 corresponds to 3 7
corresponds to 711 corresponds to B and
then B corresponds to 3 so writing it in
this order we could see that it's going
to give us this again 3 7 B 3 and so
that's how you can convert a decimal
number to a hexadecimal number use in
both techniques