Test: Adders - 2 - Electrical Engineering (EE) MCQ

Concept:

A binary adder is a logic circuit in the form of a half adder and full adder which is used to add the binary digits. 

Explanation:

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.

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

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 figure:

Important Point
The truth table of a full adder logic is:

The Sum output bit of a full adder is given by:

S = A ⊕ B ⊕ C

The carry output bit of a full adder is given by:

X₁ = AB + BC + AC

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 figure:

Important Point
The truth table of a full adder logic is:

The Sum output bit of a full adder is given by:

S = A ⊕ B ⊕ C

The carry output bit of a full adder is given by:

X₁ = AB + BC + AC

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:

Important Point
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:

The truth table of a full adder logic is:

The Sum output bit of a full adder is given by:

S = A ⊕ B ⊕ C

The carry output bit of a full adder is given by:

X₁ = AB + BC + AC

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:

Important Point
The truth table of a full adder logic is:

The Sum output bit of a full adder is given by:

S = A ⊕ B ⊕ C

The carry output bit of a full adder is given by:

X₁ = AB + BC + AC
Multiplexers:

• A multiplexer is Many to one data selector.
• A multiplexer selects one of the many data available at its input depending on the bits on the select line.
• For 2^m inputs, there are m select lines that determine which input is to be connected to the output, i.e.

Number of control lines = log2(number of input lines)
Important Point
Sequential Circuits: The block diagram shown below explains this:

The memory elements used are flip flops or latches.

Shift Register: A shift register has the capability to store one bit and if another bit is to store, in such situation it deletes the previous data and stores them. There are four kinds of shift registers:

• Serial-In Serial Out
• Serial-In Parallel Out
• Parallel-In serial Out
• Parallel-In Parallel Out

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.

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 basically made up of and a AND gate with an 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.

Sum (S) = A⊕B, Carry = A.B

Important Point
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:

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.