Adder, Half Adder and Full Adder in Digital Electronics

(Last Updated On: April 22, 2020)

Description:

Adder in Digital Electronics:

Adder- A combinational circuit that performs the addition of bits is called an Adder. Each computer has an adder located in its CPU(ALU) that is responsible for the process of addition. There are two types of Adder. They are also used in other parts of the processor, where they are used to calculate addresses, table indices, increment and decrement operators and similar operations.

  • Half Adder
  • Full Adder


Half Adder:

A combinational circuit that performs the addition of two bits is called a Half Adder. It receives two inputs and produces two outputs Sum and Carry. The block diagram for a half adder is as follows.

adder

Designing of Half Adder:

Designing of Half Adder involves the following steps.

  1. Problem: addition of two bits.
  2. The number of available inputs are two.
  3. The input and output variables are assigned letter symbols. Let’s represent the inputs by A AND B, and the outputs SUM and Carry by S and C respectively.
  4. Truth Table

adder



adder

  • Simplified Boolean function.

The Sum and Carry are in simplified form and further it cannot be simplified.

adder

Half Adder Logical Diagram:

adder

We can also obtain the logical diagram for Sum and Carry by using the Exclusive OR gate.

adder

Full Adder:

A combinational circuit that performs the addition of three bits is called a Full Adder. It receives three inputs and produces two outputs Sum and Carry. The Block diagram for the Full Adder is shown below.

adder

Designing of Full Adder:

The designing of Full Adder involves the following steps.

  • Problem: Addition of three Bits.
  • The number of available inputs are three.
  • The input and output variables are assigned letter symbols. Let we represent the inputs by A, B, and C; and the outputs by S and C i.e. S for Sum and C for Carry.
  • Truth Table

adder

adder

  • Simplified Boolean function.

Now let’s check if we can further simplify the Boolean functions of the Sum and Carry using the  Karnaugh Map K Map.

adder

 

 

The Boolean function for Sum cannot be further simplified.

adder

Now, we will simply the Boolean function of the Carry using the Karnaugh Map K Map.

adder

Carry = C = AC + AB + BC

Full Adder Logical Diagram:

adder

The logical Diagram for Sum can also be obtained by using the Exclusive OR Gate.

adder

We can also design a Full Adder by using two Half Adders.



Full adder block diagram using two half adders

adder

Logical Diagram of the Full Adder using two Half Adders:

adder

 

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My name is Shahzada Fahad and I am an Electrical Engineer. I have been doing Job in UAE as a site engineer in an Electrical Construction Company. Currently, I am running my own YouTube channel "Electronic Clinic", and managing this Website. My Hobbies are * Watching Movies * Music * Martial Arts * Photography * Travelling * Make Sketches and so on...

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