Difference between Half Adder and Full Adder
In this article, we will go through the Difference between the Half adder and Full adder, First, we will briefly describe what is half and full adders with their logical expressions and truth table, and then we will go through their differences between them, At last we will conclude our article with some FAQs.
Table of Content
- What is Half Adder?
- What is Full Adder ?
- Half Adder Vs Full Adder
- Conclusion
- FAQs
What is Half Adder?
Half Adder is a combinational logic circuit that is designed by connecting one EX-OR gate and one AND gate. The half-adder circuit has two inputs: A and B, which add two input digits and generate a carry and a sum.
Half Adder
The output obtained from the EX-OR gate is the sum of the two numbers while that obtained by AND gate is the carry. There will be no forwarding of carry addition because there is no logic gate to process that. Thus, this is called the Half Adder circuit.
Logical Expression of Half Adder
The Logical Expression for half added is given as
Sum = A XOR BCarry = A AND B
Truth Table of Half Adder
The Truth Table for Half Added is Given as
What is Full Adder ?
Full Adder is the circuit that consists of two EX-OR gates, two AND gates, and one OR gate. Full Adder is the adder that adds three inputs and produces two outputs which consist of two EX-OR gates, two AND gates, and one OR gate. The first two inputs are A and B and the third input is an input carry as C-IN. The output carry is designated as C-OUT and the normal output is designated as S which is SUM.
Full Adder
The equation obtained by the EX-OR gate is the sum of the binary digits. While the output obtained by AND gate is the carry obtained by addition.
Logical Expression of Full Adder
Given Below is the Logical Expression of Full Adder
SUM = (A XOR B) XOR Cin = (A ⊕ B) ⊕ Cin
CARRY-OUT = A AND B OR Cin(A XOR B) = A.B + Cin(A ⊕ B)
Truth Table of Full Adder
Given Below is the truth Table of Full Adder
Difference Between Half Adder and Full Adder
Given Below is the Difference between the Half adder and Full adder
| Parameters | Half Adder | Full Adder |
|---|---|---|
| Description | Half Adder is a combinational logic circuit that adds two 1-bit digits. The half adder produces a sum of the two inputs. | A full adder is a combinational logic circuit that performs an addition operation on three one-bit binary numbers. The full adder produces a sum of the three inputs and carry value. |
| Previous carry | The previous carry is not used. | The previous carry is used. |
| Inputs | In Half adder, there are two input bits ( A, B). | In full adder, there are three input bits (A, B, C-in). |
| Outputs | The generated output is of two bits-Sum and Carry from the input of 2 bits. | The generated output is of two bits-Sum and Carry from the input of 3 bits. |
| Used as | A half adder circuit cannot be used in the same way as a full adder circuit. | A full adder circuit can be used in place of a half adder circuit. |
| Feature | It is simple and easy to implement | The design of a full adder is not as simple as a half adder. |
| Logical Expression | Logical Expression for half adder is : S=a⊕b ; C=a*b. | Logical Expression for Full adder is : S=a⊕b⊕Cin; Cout=(a*b)+(Cin*(a⊕b)). |
| Logic gates | It consists of one EX-OR gate and one AND gate. | It consists of two EX-OR, two AND gates, and one OR gate. |
| Applications | It is used in Calculators, computers, digital measuring devices, etc. | It is used in Multiple bit addition, digital processors, etc. |
| Alternate name | There is no alternate name for half adder. | Full adder is also known as ripple-carry adder. |
Conclusion
In this article we have gone through the half adder and full adder in brief with their logical expression and truth, we have also seen difference between them in detail.
Difference between Half Adder and Full Adder – FAQs
Can a full adder be cascaded to add numbers larger than three bits?
Yes, The full adder can be cascaded together to create adders for numbers larger than three. This type of cascading is done to create multi bit adders such as 4-bit,8-bit or for larger bits.
How does the carry-lookahead adder differ from a conventional ripple-carry adder in terms of speed and complexity?
The Carry-lookahead adder has less propagation delay as compared to Conventional ripple-carry adder which results in faster addition operation.
What are the implications of using XOR gates in the logical expression of a full adder?
XOR gate is used for the full adder’s logical expression for calculating the sum of the input bits.
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