Test: Adders - GATE MCQ

Half Adder:

• It is a Combinational Logic Circuit with two inputs and two outputs.
• It is the basic building block for the addition of two single-bit numbers.
• The half-adder circuit is designed to add two single-bit binary numbers.
• The outputs of the circuit are Sum and Carry.
• XOR gate is used to realize Sum.
• AND gate is used to realize Carry. 

Fig: Representation of Half Adder

Truth Table of Half Adder

Fig: Logical Circuit Diagram of Half Adder

Concept:

Combinational Circuit: Combinational circuit is a circuit in which we combine the different gates in the circuit, for example, Half adder, Full Adder, Half Subtractor, Full Subtractor, encoder, decoder, multiplexer, and demultiplexer.

→ Half Adder:

Boolean expressions for Sum and Carry (if A and B are the inputs)

Sum = A'B + AB' = ( A ⨁ B)

Carry= AB

→ Full Adder:

Boolean expressions for Sum and Carry (if A, B and C are the                           inputs)

Sum = A'B'C + A'BC' + AB'C' + ABC

Carry= AB + BC + AC

→ Half Subtractor:

 Boolean expressions for Difference and Borrow (if A and B are the                    inputs)

Difference = A'B + AB' = ( A ⨁ B)

Borrow = A'B

Analysis:

From the given circuit diagram

    X = [(A'B)' . (AB')']'

⇒ X = [(A + B') . (A'+B)]' [∵ (AB)' = (A' + B')]

⇒ X = [ AB + A'B']' = ( A ⨀ B)' = ( A ⨁ B)

    Y = ( A' + B')' = AB

Obtained boolean expression refers to Half Adder.

A half adder circuit is made up of an AND gate with an XOR gate as shown below:

• A half adder is also known as XOR gate because XOR is applied to both inputs to produce the sum
• Half adder can add only two bits (A and B) and has nothing to do with the carry
• If the input to a half adder has a carry, then it will neglect it and adds only the A and B bits
• That means the binary addition process is not complete and that's why it is called a half adder

Sum (S) = A⊕B, Carry = A.B

The basic block diagram for a Full Adder is as shown:

A Full adder can be realized using two half adders as shown:

We, therefore, conclude that a full adder combinational circuit has 3 inputs and 2 outputs.

A full adder can be implemented using 2 XOR, 2 AND, 1 OR as shown in figure:

A half adder circuit is basically made up of and a AND gate with an XOR gate as shown below.

• A half adder is also known as XOR gate because XOR is applied to both inputs to produce the sum
• Half adder can add only two bits (A and B) and has nothing to do with the carry
• If the input to a half adder has a carry, then it will neglect it and adds only the A and B bits
• That means the binary addition process is not complete and that's why it is called a half adder

Sum (S) = A⊕B, Carry = A.B

The truth table for half adder is given below:

Concept:

A half adder circuit is basically made up of and a AND gate with XOR gate as shown below.

• A half adder is also known as the XOR gate because XOR is applied to both inputs to produce the sum.
• Half adder can add only two bits (A and B) and has nothing to do with the carry.
• Half adder has two inputs (A and B) and two outputs (S and C).
• If the input to a half adder has a carry, then it will neglect it and adds only the A and B bits.
• That means the binary addition process is not complete and that's why it is called a half adder.

Half adder circuit:

Half adder circuit has 2 inputs and 2 outputs.

A half adder circuit is basically made up of an AND gate and an XOR gate as shown below:

Sum (S) = A⊕B

Carry = A.B

The truth table is as shown:

A full adder circuit has three binary digit inputs (two input bits and one carry input bit) and two binary digit outputs, Sum bit and carry output bit.

A Full adder can be realized using two half adders as shown:

A full adder can be implemented using 2 XOR, 2 AND, 1 OR as shown in the figure:

Combinational Logic circuits are circuits for which the present output depends only on the present input, i.e. there is no memory element to store the past output.

A combinational circuit can have ‘n’ number of inputs and ‘m’ number of outputs as shown:

Full Adder:

• It is a combinational circuit used for the addition of binary numbers.
• It can add two one-bit numbers A and B, and carry C.
• The full adder is a three-input and two output combinational circuit.

The basic block diagram for a Full Adder is as shown:

A Full adder can be realized using two half adders as shown:

A full adder can be implemented using 2 XOR, 2 AND, 1 OR as shown in figure: