What is Decoder? Explain how combinational circuits like full adder can be implemented with decoder.

Decoder:

A decoder is a combinational circuit that converts a set of input signals into a unique set of output signals. The input signals typically represent a code, and the output signals represent the decoded value of the code. Decoders are used in a variety of applications, including data communication, digital control systems, and computer arithmetic.

Types of Decoders:

There are many different types of decoders, each with its own unique characteristics. Some of the most common types of decoders include:

• Binary Decoders: Binary decoders convert a binary code into a set of output signals, with one output signal for each bit in the code.
• Decimal Decoders: Decimal decoders convert a decimal code into a set of output signals, with one output signal for each digit in the code.
• Hexadecimal Decoders: Hexadecimal decoders convert a hexadecimal code into a set of output signals, with one output signal for each digit in the code.

Decoder Implementation Using Full Adder:

A full adder is a combinational circuit that adds two binary numbers and generates the sum and carry-out. Full adders can be used to implement decoders by connecting the inputs of the full adder to the input signals of the decoder and connecting the outputs of the full adder to the output signals of the decoder.

For example, a 2-to-4 decoder can be implemented using two full adders. The inputs of the first full adder are connected to the two input signals of the decoder, and the inputs of the second full adder are connected to the output of the first full adder and the carry-in signal. The outputs of the two full adders are connected to the four output signals of the decoder.

Advantages of Decoder Implementation Using Full Adder:

There are several advantages to implementing decoders using full adders:

• Simplicity: The full adder is a very simple circuit, which makes it easy to implement decoders using full adders.
• Low Cost: Full adders are inexpensive to manufacture, which makes decoders implemented using full adders very cost-effective.
• High Speed: Full adders are very fast, which makes decoders implemented using full adders very fast.

Applications of Decoder Implemented Using Full Adder:

Decoders implemented using full adders are used in a variety of applications, including:

• Data Communication: Decoders are used to convert data signals from one code to another.
• Digital Control Systems: Decoders are used to control digital devices.
• Computer Arithmetic: Decoders are used to perform arithmetic operations in computers.