What is
adder? Explain both of the adder (Half & Full) with proper circuit diagram
and truth table.
Title:
What is adder? Explain both of the adder
(Half & Full) with proper circuit diagram and truth table.
Introduction:
An adder is a digital logic
circuit in electronics that implements addition of numbers. In
many computers and other types of processors, adders are used to calculate
addresses, similar operations and table indices in the ALU and also in other
parts of the processors. These can be built for many numerical
representations like excess-3 or binary coded decimal.
Types of adder
1.
Half Adder
2.
Full Adder
Half Adder:
The Half Adder is
a digital device used to add two binary bit 0 and 1. The
half adder outputs a sum of the two inputs and a carry value.
Half adder truth table:
INPUTS
OUTPUTS
A
B
SUM
CARRY
0
0
0
0
0
1
1
0
1
0
1
0
1
1
0
1
Now it has been cleared that, 1-bit
adder can be easily implemented with the help of the XOR Gate for the output
‘SUM’ and an AND Gate for the ‘Carry’. When we need to add, two 8-bit bytes
together, we can be done with the help of a full-adder logic. The half-adder is
useful when you want to add one binary digit quantities. A way to develop
a two-binary digit adders would be to make a truth table and reduce it.
When you want to make a three binary digit adder, do it again. When you decide to
make a four digit adder, do it again. The circuits would be fast, but
development time is slow.
The Boolean logic for the
sum (in this case S) will be A'B+AB' whereas
for carry (C) will be AB.
Full
Adder:
The full adder circuit has three inputs:
A, B and C, which add the three input numbers and generate a carry and sum. The
full adder adds 3 one bit numbers, where two can be referred to as operands and
one can be referred to as bit carried in. And produces 2-bit output, and these
can be referred to as output carry and sum.
This adder is difficult to
implement than a half-adder. The difference between a half-adder and a
full-adder is that the full-adder has three inputs and two outputs, whereas
half adder has only two inputs and two outputs. The first two inputs are A and
B and the third input is an input carry as C-IN. When a full-adder logic is
designed, you string eight of them together to create a byte-wide adder and cascade
the carry bit from one adder to the next.
Full
adder truth table:
INPUTS
OUTPUTS
A
B
CIN
COUT S
0
0
0
0
0
0
0
1
0 1
0
1
0
0
1
0
1
1
1
0
1
0
0
0
1
1
0
1
1
0
1
1
0
1
0
1
1
1
1
1
The output carry is
designated as C-OUT and the normal output is designated as S.
With the
truth-table, the full adder logic can be implemented. You can see that the
output S is an XOR between the input A and the half-adder, SUM output with B
and C-IN inputs. We take C-OUT will only be true if any of the two inputs out
of the three are HIGH. So, we can
implement a full adder circuit with the help of two half adder circuits. At
first, half adder will be used to add A and B to produce a partial Sum and a
second half adder logic can be used to add C-IN to the Sum produced by the
first half adder to get the final S output. If any of the
half adder logic produces a carry, there will be an output carry. So, COUT will
be an OR function of the half-adder Carry outputs. Take a look at the
implementation of the full adder circuit shown below. The
implementation of larger logic diagrams is possible with the above full adder
logic a simpler symbol is mostly used to represent the operation. Given below
is a simpler schematic representation of a one-bit full adder. A full adder can be
implemented in many different ways such as with a custom transistor-level circuit or composed of other
gates. One example implementation is with. With this type of symbol, we can add two bits
together, taking a carry from the next lower order of magnitude, and sending a
carry to the next higher order of magnitude. In a computer, for a multi-bit
operation, each bit must be represented by a full adder and must be added
simultaneously. Thus, to add two 8-bit numbers, you will need 8 full adders
which can be formed by cascading two of the 4-bit blocks.
Summary:
Combinational
circuit combines the different gates in the circuit for example encoder,
decoder, multiplexer and demultiplexer Characteristics of
combinational circuits are as follows.
·
The
output at any instant of time, depends only on the levels present at input
terminals.
·
It
does not use any memory. The previous state of input does not have any effect
on the present state of the circuit.
·
It can
have a number of inputs and m number of outputs.
Conclusion:
The relationship between the Full-Adder and
the Half-Adder is half adder produces results and full adder uses half adder to
produce some other result. Similarly, while the Full-Adder is of two
Half-Adders, the Full-Adder is the actual block that we use to create the
arithmetic circuits.
Reference:
FULL ADDER USING HALF ADDER by EduNIC
education
Minimum cost fault tolerant adder circuits in
reversible logic synthesis pdf
COMPUTER ORGANIZATION AND ARCHITECTURE by
Prof. V. Kamakoti
