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Introduction
An Adder is a gadget which can add two binary numbers. It is a digital circuit that executes the function of adding two numbers. It is designed to perform the addition of binary numbers. Still, it can also be used in various other applications, such as addresses table index calculation, encoded binary codes, etc.
There are two kinds of Adder: Full Adder and Half Adder.
The primary difference between half adder circuits and full adder circuits is that the half adder circuit works by adding two 1-bit numbers. The full adder circuit is responsible for adding three 1-bit numbers. The complete description of the two kinds of the adder is right below.
What is Half Adder?
If we talk about Half Adder, it is a logic circuit that you can combine and connect one EX-OR gate and an AND gate to construct it. Half adder circuits have two inputs, A and B. These add 2 different input numbers and produce a sum and carry.
The output from the EX-OR gate is the total of two numbers, whereas the output produced by the AND gate is famous as the name “carry.” There is no carry additional forwarding since no logic gate is present there that can process it. Therefore, it is referred to as “the Half Adder circuit.
Logical Expression :
Sum = A XOR B
Carry = A AND B
What is Full Adder?
If we talk about the Full Adder, it is the circuit containing two EX-OR gates, two gates for AND, and an OR gate. Also, Full Adder adds 3 different inputs and generates two outputs: two AND gates, two EX-OR gates, and one OR gate. The two inputs are A & B.
Also, there is a third input designated as C-IN. Its output is identified as C-OUT. In addition, the standard output is designated as S, and that’s a SUM.
The equation derived using the EX-OR gate represents the total of binary numbers. The output generated by the AND gate is the carry gained by addition.
Logical Expression :
SUM = (A XOR B) XOR Cin = (A B) Cin
CARRY-OUT = A AND B OR Cin(A XOR B) = A.B Cin(A B)
Key Differences in Half Adder and Full Adder
- Half adder is a binary addition and produces sum and carry bits. On the other hand, Full adder can add three binary digits and creates a sum and carry bit.
- The hardware structure for Half Full Adders differs from one another. Half Adder contains just one EX-OR gate and one AND gate. On the other hand, the complete adder comprises two EX-OR gates and an AND gate with one OR gate.
- One more major difference between Half and Full Adder is that the results from the recent addition can’t be added to the next one when using half adder. In contrast, the full adder can also add the previous carry with the present time inputs.
A complete adder circuit is the heart of most digital circuits that do subtraction or addition. It’s named this because it joins two binary digits and one carry-in to generate addition and carry-out digits. A half adder lets us multiply two binary numbers with single digits and produces an output of two numbers. The name is because of the combination of two half adders together, and using an OR gate produced an entire adder. It only performs half the work as a full adder. It serves to add two bits by carrying. Therefore, a full adder can add three bits.
In the above discussion, it is apparent that there are a variety of variations between a half-adder and a full-adder circuit. But, both half-adder and full circuits form the foundational components of many digital circuits.
Also, we can use these to perform arithmetic functions like calculators, electronic measuring instruments, computer systems, digital processors, etc. One of the primary advantages of using the half/full adders in digital circuits is that they’re constructed by making use of logic gates to process input data very quickly.
The average processing speed of logic gates is in the range of ms (microseconds). Thus, we generally use half and full-adder circuits when performing calculations at high speeds.
