Test: Combinational Logic Circuits

An encoder converts information from one format or code to another. An encoder can be used to encode the decimal number to binary number.

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

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 2m inputs, there are m select lines that determine which input is to be connected to the output.

Concept:

• A decoder is a combinational logic constructed with logic gates.
• It is the reverse of the encoder.
• A decoder circuit is used to transform a set of digital input signals into an equivalent decimal code of its output. For ‘n’ inputs a decoder gives ‘2n’ outputs.
• Block diagram of the Decoder is shown below:

Decoder expansion

n1 × m1 → n2 × m2

The number of D2 decoder required is given as:

∑ K = K₁ + K₂ + K₃ + ------ 

Calculation:

One 2:4 decoder and four 3:8 decoders can represent 5:32 decoder in the following way:

Hence option (A) is the correct answer.

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

Combinational Logic circuits:

The Combinational Logic circuits are circuits for which the present output depends only on the present input.

There is no memory element to store the past output.

It performs an operation that can be specified logically by a set of Boolean functions.

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

Hence, All the above statements are correct.

Sequential Circuits: The block diagram shown below explains this:

The memory elements used are flip flops or latches.

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

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:

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