Test: Half Adder - Electrical Engineering (EE) MCQ

Half Adder using NAND Gates:
The half adder can also be designed with the help of NAND gates. NAND gate is considered as a universal gate. A universal gate can be used for designing any digital circuitry. It is always simple and efficient to use the minimum number of gates in the designing process of our circuit. The minimum number of NAND gates required to design a half adder is 5.

• The first NAND gate takes the inputs which are the two 1-bit numbers.
• The resultant NAND-operated inputs will be again given as input to 3- NAND gates along with the original input. 
• Out of these 3 NAND gates, 2-NAND gates will generate the output which will be given as input to the NAND gate connected at the end.
• The gate connected at the end will generate the sum bit. Out of the 3 considered NAND gates, the third NAND gate will generate the carry bit.

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:

The truth table for half adder is given below:

Therefore, the carry is given by AB.
Hence the carry output is high if the both inputs are high i.e. 1,1

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

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. 

Half adder: it is a logic circuit that performs addition on two binary digits. It produces a sum and carry. 

Full adder: It is a logic circuit that takes three inputs to perform addition. Two binary input and one carry-in input of the previous stage is used. It generates sum and carry (C-out). C-in is a carry from a less significant digit and c-out is a carry from the most significant bit.

If we want to add two n- bit binary adders then it requires 1 half adder and n-1 full adder to complete the circuit. So, in the given question to add 4- bit binary numbers requires 1 half adder and 3 full adders.

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.

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

Obtained boolean expression refers to Half Adder.

Half adder circuit have two inputs and two outputs (sum and carry).

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

Concept:
A logic circuit that can perform addition of 2-bits is the HALF ADDER. 
It is used to add 2-bits using using one EXOR gate where as carry operation can be performed using AND gate.

Analysis:
Let the two inputs are A and B . Outputs are Sum and Carry Out.

SUM = EXOR(A,B)
CARRY OUT = AND(A,B)