Difference Between Half Adder and Full Adder
Major aistinguishing point betwwen half adder and full adder is that a half adder consists of only one AND gate and EX-OR gate. A full adder consists of one OR gate and two EX-OR and AND gates. The difference between the half adder and full adder is based on various metrics and parameters, which are explained below.
Key Differences Between Half Adder and Full Adder
Metrics | Half Adder | Full Adder |
Primary | The Half Adder is a type of combinational logic circuit that adds two 1-bit binary digits. It generates carry and sum for the inputs. | The Full Adder is a type of combinational logic that adds binary digits. It generates the sum of all three inputs along with a carrying value. |
Addition of the Previous Carry | The Half Adder does not add the carry obtained from the previous edition. | With its current inputs A and B, the Full Adder also adds the previous carry. |
Hardware Structure | A Half Adder consists of only one AND gate and an EX-OR gate. | A Full Adder consists of an OR gate and two EX-OR and AND gates. |
Inputs | There are two inputs in a Half Adder- A and B. | There are a total of three inputs in a Full Adder- A, B, and C-in. |
Features | The Half Adder is good for digital measuring devices, computers, calculators, etc. | The Full Adder comes into play in various digital processors, adding multiple bits, etc. |
What is a Half Adder?
It is a combinational logic circuit that uses two logic gates: an AND gate and an EX-OR gate. It consists of two inputs, says A and B; after adding these two inputs, the output is generated in the form of carrying and sum; therefore, there are two output terminals. The sum is generated using the Ex-OR gate, and the carry is generated using the AND gate.
Difference between Half Adder and Full Adder PDF
The logical expressions for sum and carry of a half adder are:
Sum (S) = A ⊕ B
Carry (C) = A.B
Truth Table for Half Adder
When we add 0 to 0, 0 to 1, and 1 to 0, we get the sum 0 and 1, respectively, and both are one-digit binary numbers. Hence, in these cases, there will be no carry during addition, or carry is 0 here. We can summarise this in a truth table for the half adder. The truth table comprising the possible outputs obtained for adding two 1-bit binary numbers using a half adder is as follows.
Input | Output | ||
A | B | CARRY | SUM |
0 | 0 | 0 | 0 |
1 | 1 | 1 | 0 |
0 | 1 | 0 | 1 |
1 | 0 | 0 | 1 |
What is a Full Adder?
A full adder is a combinational circuit used to perform the addition of two n-bit binary numbers. It uses two AND gates, two EX-OR gates, and one OR gate to perform addition. It adds three binary numbers, namely Cin, the carry generated from the previous addition; Cout, the carry generated by the addition of present inputs A and B; and Sum, the addition of the inputs A and B.
A full adder can also be designed using two half adders and an OR gate, where the OR gate is responsible for generating the carry, and Half adders are responsible for generating the sum of the two binary numbers. The logical expression for sum and carry using the full adder is:
CARRY-OUT = AB + BCin + ACin
Sum = (A ⊕ B) ⊕ Cin
Truth Table for Full Adder
The full adder is a 'combinational circuit' that can execute addition on three input bits or two inputs plus the carry-in from the preceding operation. The truth table comprising the possible outputs obtained for adding two binary numbers using a full adder is as follows.
Input | Output | |||
A | B | C | SUM | CARRYOUT |
0 | 0 | 0 | 0 | 0 |
1 | 1 | 1 | 1 | 1 |
0 | 1 | 1 | 0 | 1 |
1 | 0 | 1 | 0 | 1 |
0 | 0 | 1 | 1 | 0 |
0 | 1 | 0 | 1 | 0 |
1 | 0 | 0 | 1 | 0 |
1 | 1 | 0 | 0 | 1 |
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