Test: Combinational Logic Circuits - GATE MCQ

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:

Combinational circuits are:

• Multiplexer/Demultiplexer
• Encoder/Decoder
• Adders
• Subtractors
• Code Converters

In a sequential circuit, the output depends on both the present and the past values. The circuit diagram is as shown:

Examples of sequential circuits:

• Shift Registers
• Flip flops
• Counters

To implement 2ⁿ × 1 MUX using 2 × 1 MUX, the total number of 2 × 1 MUX required is (2ⁿ - 1).

∴ The number of 2 × 1 multiplexer required to implement 16 × 1 MUX will be:

n = 16 - 1 = 15

Or we can follow the below steps to calculate the same:

1^st stage = 16/2 = 8

2^nd  stage = 8/2 = 4

3^rd stage = 4/2 = 2

4^th stage = 2/2 = 1

The sum will give the total number of MUX required to implement 16 × 1 multiplexer using 2 × 1, i.e.

n = 8 + 4 + 2 + 1 = 15

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:

Therefore, the carry is given by AB.

Hence the carry output is high if the both inputs are high i.e. 1,1

Solution: An encoder is a combinational logic circuit that converts an active input signal into a binary code corresponding to the input.

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.

A full adder uses XOR gates for the sum and AND gates for the carry. It adds three input bits, including the carry-in.

Concept:

Multiplexer:

• It is type of combinational circuit for which the present output depends only on the present input.
• It is also known as memoryless circuit because there are no memory element to store the past output.
• A multiplexer is a many to one data selector.
• It selects one of the many data available at its input depending on the bits of the select lines.
• For 2ⁿ inputs, there are n select lines that determine which input is to be connected to the output.

In the given multiplexer circuit, we have 8 input lines.

∴ 2ⁿ = 8

2ⁿ = 2³

By comparing exponents on both sides we get;

n = 3

In conclusion, the total number of select lines is (n) = 3

A half adder is a basic digital circuit used to add two single-bit binary numbers. It consists of two outputs: Sum and Carry.

• The Sum output is generated by an XOR gate because XOR (exclusive OR) produces a high (1) output when exactly one of the inputs is high. This matches the behavior of binary addition where the sum is 1 when exactly one of the bits is 1.
• The Carry output is generated by an AND gate, which outputs 1 only when both inputs are 1, representing the carry-over in binary addition.

So, a half adder requires both an XOR gate for the sum and an AND gate for the carry.

Combinational circuits do not depend on previous outputs; their output depends only on the present input. Sequential circuits, on the other hand, depend on both present input and past outputs.