Half Adder Video Lecture | Analog and Digital Electronics - Electrical Engineering (EE)

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hi friends in this video we will be
talking about the adder circuit if you
have been following our channel you
would remember that we have covered a
video which walks you through the
addition of binary numbers typically
addition of binary numbers gives us the
sum term and the carry if in case you
need to revise your concepts of adding
binary numbers the link is provided in
the description below but don't you
worry this video will be sufficient to
get the drift of the concept so getting
back to this video adders are basic
building blocks of any digital
electronic device you can use them to
make your own calculator other circuits
make arithmetic and logical circuits
called ALU to compute the binary
addition operation on bits of theta
adults are of different types
starting from half adders full adders
and ripple carry adder z' let us
understand the half adder the half adder
circuit is useful when you want to add
one bit of numbers we all know by now
one bit takes two values zero or one let
us refer to the classic truth table that
we all use when two variables a and B
are of one bit each here some indicates
the value operated upon addition and
carry indicates whether there has been a
carry or not by adding the two numbers
let's add them 0 plus 0 is 0 with of
course no carry 0 plus 1 is 1 with no
carry
1 plus 0 is 1 again with no carry
however one plus 1 as we know in binary
systems the sum is 0 and there is a
carry of 1 also there is one more trick
to find this if the number of terms to
add contain odd number of ones the sum
is 1 and for even number of ones the sum
is 0 and Gary is 1 now I want you all to
analyze a truth table for some we see
that when variables a and B are both 0
or 1 sum is 0 and when a is 0 and B is 1
or 4 a is 1 and B 0 the output is 1 this
is the truth table for the XOR gate
let's present this equation using the
XOR gate let's take a and B and connect
to an XOR gate the output is the sum
term a XOR B now analyze the truth table
for just the carry section if you all
remember the video on basic gates this
is the truth table for an gate let's
represent it using a NAND gate and
that's a carry expression another way we
can find the boolean expression is by K
map let's represent this column which is
for the carry using it we will take a 2
input K map the inputs being a and B
let's update it group it and write the
boolean expression here 1 is present for
a and B the expression for carry is a
and B let's update the came up for some
let's group the terms
well no grouping here and write the
expression for this term this is a and B
bar since a is 1 and B is 0
so while writing the SOP or sum of
products we represent it as a and B bar
this term here is a bar and B we will
take both these terms and sum them Thurs
writing the sum of the products
expression
a and B bar or a bar and B is nothing
but a X or B and that is our sum
expression and if he noticed the came up
for some it is quite peculiar it
represents a check board configuration
here no grouping is possible since the
ones are represented in the check board
style if you see a came up like this
simply XOR the terms in this case it is
a XOR B you can write the boolean
expression for this and solve it and
derive to the same answer a half adder
is built using just two gates an and
gate to give us a carry term and the XOR
gate to give the sum term one more thing
to remember is that the half adder does
not take carry from the previous sum the
answer to this is that the variables are
just one bit hope you have understood
the half adder circuit in the next video
we will see full adders
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