Explain Half Adder and Full Adder with Truth Table

Explain Half Adder and Full
Adder with Truth Table

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Explain Half Adder and Full Adder with
Truth Table
 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.
Introduction

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Adders Are Classified Into Two Types
 Half Adder and Full Adder .
 The half adder circuit has two inputs: A and B.
 It add two input digits and generate a carry and sum.
 The full adder circuit has three inputs: A, B and C.
 It add the three input numbers and generate a carry and sum.

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Adders Are Classified Into Two Types

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What is Half Adder and Full Adder Circuit
 The half adder adds two binary digits called as augend and addend.
 Half adder produces two outputs as sum and carry.
 XOR is applied to both inputs to produce sum.
 OR gate is applied to both inputs to produce carry.

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What is Half Adder and Full Adder Circuit
 The full adder adds 3 one bit numbers.
 Where two can be referred to as operands.
 One can be referred to as bit carried in.
 It produces 2-bit output, and these can be referred to as output
carry and sum.

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Half Adder
 Using Half Adder, you can design simple addition with the help
of logic gates.
 Let’s see an addition of single bits.
0+0 = 0
0+1 = 1
1+0 = 1
1+1 = 10

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Half Adder
 These are the least possible single-bit combinations. But the result for 1+1
is 10, the sum result must be re-written as a 2-bit output. Thus, the
equations can be written as
0+0 = 00
0+1 = 01
1+0 = 01
1+1 = 10
 The output ‘1’of ‘10’ is carry-out. ‘SUM’ is the normal output and ‘CARRY’
is the carry-out.

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Half Adder

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Half Adder Truth Table
 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’.

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 When we need to add, two 8-bit bytes together, it 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.

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Image Of Half Adder Logic Circuit

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 The simplest expression uses the exclusive OR function
Sum=AÅB
 An equivalent expression in terms of the basic AND, OR, and NOT is
SUM=A|.B+A.B’

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VHDL Code For half Adder:
entity ha is
Port (a: in STD_LOGIC;
b : in STD_LOGIC;
sha : out STD_LOGIC;
cha : out STD_LOGIC);
end ha;
Architecture Behavioral of ha is
begin
sha <= a xor b ;
cha <= a and b ;
end Behavioral

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Full Adder
 Full 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.

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Full Adder
 The output carry is designated as C-OUT and the normal output is
designated as S.

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Full Adder Truth Table
 The full adder logic can be implemented with the truth table.
 The output S is an XOR between the input A and the half-adder, SUM
output with B and C-IN inputs.
 Take C-OUT will only be true if any of the two inputs out of the three are
HIGH.

Truth Table

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Full Adder Logic Circuit
 We can implement a full adder circuit with the help of two half adder circuits.
 First, half adder will be used to add A and B to produce a partial Sum.
 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.

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 If any of the half adder logic produces a carry, there will be an output carry.
 A COUT will be an OR function of the half-adder Carry outputs.
 The implementation of larger logic diagrams is possible with full adder logic.
 A simpler schematic representation of a one-bit full adder.

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Simpler Schematic Representation of a One-Bit Full Adder
Full Adder Design Using Half Adders
 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.

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 In a computer, for a multi-bit operation.
 Each bit must be represented by a full adder and must be added
simultaneously.
 To add two 8-bit numbers, you will need 8 full adders which can be formed
by cascading two of the 4-bit blocks.
 Combinational circuit combines the different gates in the circuit.
 Example are encoder, decoder, multiplexer and de multiplexer.

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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.

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The relationship between the Full-Adder and the Half-Adder:
 Half adder produces results and full adder uses half adder to produce
some other result.
 Similarly, the Full-Adder is of two Half-Adders.
 The Full-Adder is the actual block that we use to create the arithmetic
circuits.

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VHDL Coding for Full Adder
entity full_add is
Port ( a : in STD_LOGIC;
b : in STD_LOGIC;
cin : in STD_LOGIC;
sum : out STD_LOGIC;
cout : out STD_LOGIC);
end full_add;

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VHDL Coding for Full Adder
Architecture Behavioral of full_add is
component ha is
Port ( a : in STD_LOGIC;
b : in STD_LOGIC;
sha : out STD_LOGIC;
cha : out STD_LOGIC);
end component;
signal s_s,c1,c2: STD_LOGIC ;
begin
HA1:ha port map(a,b,s_s,c1);
HA2:ha port map (s_s,cin,sum,c2);
cout<=c1 or c2 ;
end Behavioral;

Explain Half Adder and Full Adder with Truth Table

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