An adder is a digital circuit that performs addition of numbers. Adders are commonly used in arithmetic logic units of computers and other processors. A half adder is a basic digital circuit that performs addition of two binary digits and outputs their sum and carry. It incorporates an XOR gate to generate the sum and an AND gate to generate the carry. A limitation of half adders is that they cannot accept a carry bit from a previous addition.

1. A N A D D E R I S A D I G I T A L C I R C U I T T H A T
P E R F O R M S A D D I T I O N O F N U M B E R S . I N M A N Y C O M P U T E R S A N D
O T H E R K I N D S O F P R O C E S S O R S A D D E R S A R E U S E D I N
T H E A R I T H M E T I C L O G I C U N I T S
adder

2. Half adder
 Half adder logic diagram
 Half adder in action
 The half adder adds two single binary digits A and B. It has two
outputs, sum (S) and carry (C). The carry signal represents
an overflowinto the next digit of a multi-digit addition. The value of
the sum is 2C + S. The simplest half-adder design, pictured on the
right, incorporates an XOR gate for S and an AND gate for C. The
Boolean logic for the sum (in this case S) will be A′B + AB′ whereas
for the carry (C) will be AB. With the addition of an OR gate to
combine their carry outputs, two half adders can be combined to
make a full adder.[1] The half adder adds two input bits and
generates a carry and sum, which are the two outputs of a half
adder. The input variablesof a half adder are called the augend and
addend bits. The output variables are the sum and carry.

3. Half adder

4. Half adder using NAND gates only.

5. Difference between Half Adder and Full Adder
 The major difference between Half Adder and Full
Adder is that Half Adder adds two 1-bit numbers
given as input but do not add the carry obtained
from previous addition while the Full Adder, along
with two 1-bit numbers can also add the carry
obtained from previous addition.

6.  Difference between Half Adder and Full Adder
 The major difference between Half Adder and Full Adder is that Half Adder adds two 1-bit
numbers given as input but do not add the carry obtained from previous addition while the Full
Adder, along with two 1-bit numbers can also add the carry obtained from previous addition.

 Half Adder and Full Adder, both are combinational logic circuit but differs in the way they
process the inputs. A combinational circuit is one which does not consist of any memory
elements; it comprises of only logic gates.
 Another significant difference between Half Adder and Full Adder is that Half Adder consists of
one EX-OR gate and one AND gate while Full Adder consists of two EX-OR gates, two AND
gates and one OR Gate. If any carry is obtained in the addition process, it is given to full adder
as an input, and it adds that carry along with other inputs. On the contrary, half adder does not
take any carry obtained from previous addition.
 The adder is the crucial digital circuit used in computers, digital processing etc. Due to the
utilization of logic gates, the addition process becomes fast. Half Adder and Full Adder, both
perform addition and are widely used in digital circuits for performing arithmetic functions.

8. Half-adders have a major limitation in that they
cannot
 Half-adders have a major limitation in that they
cannot accept a carry bit from a previous stage,
meaning that they cannot be chained together to
add multi-bit numbers. However, the two output bits
of a half-adder can also represent the result A+B=3
as sum and carry both being high.

10.  Full Adder is the circuit which consists of the circuit
which consists of two EX-OR gates, two AND gates
and one OR gate.

11.  Half Adder is a combinational logic circuit
which is designed by connecting one EX-OR
gate and one AND gate. It adds two one-bit
numbers and generate the sum as the output.