Combinational Logic Circuits - Free MCQ Practice Test with solutions, GATE

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.