Combinational circuits are one of the primary components of digital electronics. Combinational circuits contain five gate types: AND, OR, NOT, NAND, and NOR. 

With the help of these gates, you can make various types of combinational circuits. These circuits are widely used in the electronics industry. 

Without having any further details, let’s get started!

Five Types of Combinational Circuits

• Half Adder Combinational Circuit

A half adder is one of the basic combinational circuits to add two single-digit binary numbers. It produces the sum bit (also known as the least significant bit) and the carry bit (also known as the most significant bit). 

The half adder is called a "half" adder because it can only add two bits and does not consider any carry input.

This type of circuit consists of two inputs, A and B. It represents the two bits to be added. Moreover, it also has two outputs, SUM and CARRY, representing the sum and carry bits, respectively. 

You can use basic logic gates such as NOR and AND gates to implement a half-adder circuit. The NOR gate is used to calculate the SUM output, while the AND gate is used to calculate the CARRY output.

• Full Adder Combinational Circuit

Full adder performs binary addition of three bits. It has two input bits (A and B) and a carry input (Cin). It produces two outputs: the sum bit (SUM) and the carry output (Cout). 

Unlike a half adder, a full adder considers the carry input from the previous addition stage, allowing it to handle carry propagation.

You can use basic logic gates such as NOR, AND, and OR gates to implement a full-adder circuit. The NOR gates are used to calculate the SUM output, while the AND and OR gates are used to calculate the Cout output. 

The inputs A, B, and C are connected to the inputs of the NOR and AND gates, and the outputs of the gates are combined using the OR gate to obtain the Cout output. The output of the NOR gates is connected to the SUM output.

• Multiplexer Combinational Circuit

A multiplexer routes data from multiple input sources to a single output line based on control inputs. It has two main components: input lines and control inputs. 

The number of input lines corresponds to the number of data sources, and the control inputs determine which input line is selected and routed to the output line. The selection process is based on the binary value of the control inputs.

A multiplexer with n input lines requires log2(n) control inputs. The control inputs determine the index of the selected input line. 

For example, if you have four input lines (A, B, C, and D), you would need two control inputs (S0 and S1) to select one of the input lines. You can use basic logic gates such as AND, OR, and NOT gates to implement a multiplexer circuit.

• Encoder Combinational Circuit

An encoder is a combinational circuit that converts multiple input lines into a smaller number of output lines. It performs the reverse function of a decoder. 

An encoder is commonly used in various applications, including data compression, address decoding, and signal multiplexing. 

Basic logic gates such as AND and OR gates are used to implement an encoder circuit. The input lines are connected to the inputs of the AND gates, and the outputs of the AND gates are combined using the OR gates to generate the encoded output on the output lines.

There are different types of encoders. The two main types of encoders are the priority encoder and the absolute encoder.

• Priority Encoder

A priority encoder is used when multiple input lines can be active simultaneously, but only the highest priority input needs to be encoded. 

It assigns a priority to each input line, and the output represents the highest-priority active input line. The priority encoder uses additional control lines to indicate the priority levels.

• Absolute Encoder

An absolute encoder, also known as a binary encoder, converts a specific input into its equivalent binary code on the output lines. 

Each input line corresponds to a specific binary value. The corresponding binary code is generated on the output lines when an input line is activated.

• Decoder Combinational Circuit

Decoder decodes binary code into human-readable form. It performs the opposite function of an encoder. 

Decoders that are widely used in various applications, including address decoding, data demultiplexing, and control logic. 

Basic logic gates such as AND and NOT are implemented to implement a decoder circuit. The input lines are connected to the inputs of the NOT gates, and the outputs of the NOT gates are connected to the inputs of the AND gates. The outputs of the AND gates represent the decoded output lines.

There are different types of decoders, including the binary decoder, the BCD (Binary Coded Decimal) decoder, and the priority decoder.

• Binary Decoder

A binary decoder is the simplest decoder, where each possible combination of input lines corresponds to a unique output line. The number of input lines and output lines is determined by the number of bits in the binary code.

• BCD Decoder

A BCD decoder decodes a Binary Coded Decimal input into its corresponding decimal output. BCD is a binary representation of decimal numbers, where a 4-bit binary code represents each decimal digit.

• Priority Decoder

A priority decoder is used when multiple input lines can be active simultaneously. Still, only the highest priority input needs to be decoded. It assigns a priority to each input line, and the output represents the highest-priority active input line. The priority decoder uses additional control lines to indicate the priority levels.

Now, let’s dive into another segment of this article, i.e. master theorem.

What is Master Theorem?

The master theorem is a technique used to analyze the time complexity of divide-and-conquer algorithms. It solves recurrence relations to do so. It provides three cases that cover common scenarios. 

These three cases help to determine the time complexity based on the sizes of subproblems. This theorem simplifies the process of estimating time complexity. However, it may not apply to all recurrence relations. 

A master theorem is a fundamental tool for understanding algorithm performance and scalability.

Conclusion

Combinational circuits are essential for almost every electronic item you use. They work with the truth table logic and five types of gates.