so what is binary number system
and why is it so famous
long ago when civilization probably
started
we humans
discovered a number system
that would have
exactly ten digits and this number
system
was called decimal number system
and the digits in this number system
would be
zero one two three four five six seven
eight and nine
not so long ago
another number system became famous
at the language of computers
and this was called
the binary number system
a binary number system
would have only two digits zero and one
if a number system has n digits we
say that
the base of the number system is n so
decimal number system can also be called
base ten number system
and similarly
binary number system can also be called
base two number system
now why does a computer
understands binary
and the simplest
explanation can be
that a computer is an electrical device
and all electrical device
understands
is electrical signals
so say for example if we have an input wire to this machine
there are only states possible for this wire
either current is flowing through this wire
or current is not flowing through this
wire
if current is flowing through this wire we say
that the state of this wire this input
is signaled
and we say that a signal state
corresponds to one
and if current is not flowing this is not signaled then we say that not signal state
corresponds to a zero
so a zero
or one
invited the actually translates to
a signal or non signal state in an
electrical device
and we can have multiple wires or multiple inputs
to represent multiple ones and zeros
now let us quickly see how we write a number
these two number system
if we write a number in decimal
number system
and if we go back to our
elementary school mathematics then
we write number in one row and multiple columns
the right most column corresponding to
the right most digit
is called the ones place
second right column is called the tens place
and we go on increasing in multiple
of tens like hundreds place and
thosounds place
and so on
if we have to the represent this
in powers of ten then
the right most place or the least significant
digit
corresponds to the ten to the power zero
and go on like ten to the power one ten to the power two ten to the power three and so on
and as we go on
towards left we go on increasing in power of tens
say for example if we write a number one twenty five in decimal number system
we say that this number has got
five ones
two tens
and one hundred
we could also say that this number has got five ten to the power zeros
two ten to the power one and one ten to the power two
and this sums up
to one twenty five
now when we write a number in binary number system
the only digits possible
are zero and one
the right most column
corresponds to the ones position
second right column corresponds to 
twos position and we go on
increasing
in powers of two like fours position eights position
and so on
and if we have to write the same thing in
powers of twos
this corresponds to two to the power zero
two to the power one
and so on
and similarly we can go on we can
keep going towards left
in powers of two
now let us write a number in binary
so let's say we become a number one one
one one
one zero one
so we say that this is got
one one
zero twos
one four and we could also say that this is got
one two the power zero
zero to the power one
and one two the power two
and we can go on
so to find out the place value of a digit
in binary number system we multiply the digit one or zero by the
corresponding power of two
so if to pick up the seventh column from
left
so the place value here is calculated by multiplying the number one
with two the power six
so we get this
so if we want to convert
a number from binary to decimal number
system it is pretty straightforward
well you need to do is
pick up all these
place values and sum of them up
and if you try to sum this up this comes as
hundred and twenty five
so one one one one
one zero one
in binary
is actually
number one twenty five in decimal number system
so we say practice number one one one
one
one zero one
in base two
is actually hundred and twenty five
in base ten
now in this lesson we did not describe
how we got this number
one one one one one zero one
in binary
for one twenty five
we will do it in the next lesson
so in the next lesson we will show you
how to convert
a number
from decimal number system
to binary number system
so thanks for watching
