Magnitude Comparator Video Lecture - Digital Electronics - Electrical Engineering

in this video we are going to learn
about magnitude comparator this
magnitude comparator for Q will be use
it to compare two 4-bit binary numbers
hence the input of the circuit will be
8-bit Darren four bits will be one
number and another four bits will be
other number the outputs of this circuit
will be less than equal to and greater
than so when we are comparing two
numbers we can give the relation between
those two numbers as a greater than B a
less than B are a equal to B so if you
are giving the block diagram of
magnitude comparator like this a and B
we are comparing because we are
representing a and B as four with
numbers J is represented as a 3 a 2 A 1
a not B 3 D 2 B 1 B not 4 B so the
output could be a less than B or a equal
to B all a greater than D so only one of
the output could be one at a time so how
we are going to determine whether two
bits are equal or not here what is the
logic behind developing the circuit for
us so when we are comparing two numbers
how can we save that when e is less than
or greater than or equal to the other
number now if I say like a3 and b3 we
are considering we are going to compare
some that is from left hand side to
right hand side so first I will compare
a 3 D tree if these two numbers are
equal then only you are going to compare
a 2 and B 2 and then if these also are
equal then we will compare a 1 and B 1
and then I are not ending up finally so
here we can say that a equal to B then a
is equal to B 3 a 2 equal to B 2 a 1
equal to B 1 a not equal to B naught so
how can we like determine whether two
bits are equal or not which gauge can be
used it is nothing but text
or gate so the expression X 3 we are
taking as an output for the expression
as a 3 d 3 bar T 3 bar plus a 3 B 3 so X
3 will become 1 then a3 and b3 are one
or both are 0 so whether a 3 B 3 are 0
or 1 if both are equal X 3 will become 1
similarly we'll say X 2 is 1 when a 2
and B 2 are equal X 1 is 1 when a 1 and
B 1 are equal and X naught is 1 when u
naught and P naught are equal so when a
all X 3 X 2 X 1 and X naught R 1 then we
can say that a equal to B so that is the
expression which shows that a is equal
to B now let us give the expression for
a greater than B so here there are
different cases where EA would be
greater than B so when we are comparing
from ll left-hand side a3 and b3 we
attempt our interest so in this case
first time itself if we want to say that
a is greater than B then a3 should be 1
and we reach in this 0 because we are
having only 2 bits ones and zeros so a3
could be 1 and B 3 is 0 this is one case
where EA can be greater than B so a 3 1
and B 3 0 means we can represent data in
the form of expression f HB b 3 dash and
the next case is we have to compare a2
and b2 they compare a 2 and V 2 when a 3
and B 3 are equal so when a 3 and B 3
are equal we can say that X 3 is used so
X 3 is 1
so X 3 here indicates that a 3 B 3 are
equal so we are comparing a 2 and B 2
bar a 2 and B 2 and similarly the other
case is X 3 X 2 R 1 that is both a 3 B 3
and a 2 B 2 are equal then we will
compare even and B 1 so this case we
will consider a 1 is 1 and D 1 is 0 so a
1 billion bar
finally last case a not b not bar so
what is the use of giving X 3 X 3 X 2 X
1 in these cases is let us see let us
consider some example as 1 0 1 1 K is 1
0 1 1 let us consider B as 0 1 0 1 so in
this case we say that a3 and b3 then we
compare KP is 1 P 3 is 0 so I will say
that a is greater than T and if I don't
include these cases what wiII happen k2
is the 0 and B 2 is 1 so in such a case
a 2 is a less than dat becoming so a
less than derailer should be 1 so if we
don't include this for the same numbers
we get a is greater than Mihai also a is
less than D so that is the reason why we
include X 3 here and x3 x2 you are and X
3 X 2 X 1 in this case similarly we can
write the expression for a less than B
so that is it lv b 0 and b will become 1
in this case so a 3 bar b 3 plus X 3 K
to power B 2 plus X 3 X 2 a 1 bar be 1
plus X 3 X 2 X 1 a naught dot v naught
is the expression for a less than B now
if we are drawing the a tube using this
three expressions a equal to B a less
greater than B a less than B then we are
going to can get this a cheaper
magnitude comparator that is how the
virtual if we can even extend this
magnitude comparator which is designed
for for big numbers to 8 bits so here as
we already know that we will be
comparing first MSD four bits so that is
X 7 by 7 X 6 by 6 X 5 y 5 X 4 y 4 will
be compared so here we will get either X
is less than 1 X equal to Y or X is
greater than Y so you need to treat
before
of this we will be considering that it
is a equal to B or F is equal to one so
these are output whatever we get from
this particular MSD magnitude comparator
will give that input as I of a is less
than greater than VI of a equal to BI of
a less than D so based on this we are
going to get the final output so suppose
if you say like this is equal to then
here this equal to and then this will be
come back finally based on this
particular result it is beginning the
output suppose if we are getting
hydrater than hi a greater than B here
itself then that way we can say that X
is greater than Y has the output of the
fine form finally also suppose if it is
a less than B then final output also
will be X less than Y if it is a equal
to B then the output depends upon LSB
for big numbers in this fashion we can
extend the number of bits to any number
required now we will see how to design
magnitude comparator using binary
parallel adder so we all know that this
is binary parallel adders which performs
subtraction operation and the comparison
we can know that it can be performed
using subtractor when we perform two's
complement subtraction we know that p
for EP case whether X is greater than Y
or X is less than Y X is greater than Y
study is stage and also it depends upon
the sum result as 3 s 3 s 1 s none so
when this is not equal to 0 and C 4
equal to 1 then we can say that X is
greater than Y so here we consider that
s 3 is 2 s 1 s naught if any one of
these is equal to 1 this output will
become 0 so here this will become 1 and
C 4 is 1 so X is greater than Y
similarly if C 4 is equal to 0 and this
is not equal to 0 then we can indicate
that it is X is less than Y if all
inputs are 0
output of the knowledge becomes one and
so the input of this and gate becomes
one C four also is one and we can say
that X is equal to one so this is the
way how we define magnitude comparator
using binary parallel subtractor