DECODER

DECODER - INTRODUCTION

The decoder is a combinational logic circuit used to convert a piece of coded information into another signal pattern.
It converts 'n' number of inputs into 'm = 2^n' number of unique outputs. Such decoders are usually described as n-line to m-line decoders. It has only one high output for any given code.

The decoder is the reverse of an encoder and the special case of a demultiplexer without the input line. Decoders can be used to do code conversions or detect the presence of a particular binary state and thereby to activate other circuits based on the input.

The simplest decoder is a single logic gate such as AND or NAND gate with input inverter, whose output activates when all the inputs are HIGH. When combined with inverters, a NAND or AND gate can create output for a unique combination of inputs. So, the decoder used in practical applications is the extension of the simplest decoder and it consists of several NOT and AND gates. The number of NOT gates required would be equal to the number of inputs ie., n. The number of AND gates required would be equal to the number of outputs ie.,m = 2^n.

2–4 DECODER

2–4 DECODER— LOGIC DIAGRAM, TRUTH TABLE, AND EQUATIONS

The above figure shows the logic diagram, truth table and equations of a simple 2–4 decoder. It converts two-bit code into a 4-bit pattern. For each combination of input word (for 2 bit, inputs are 00,01,10 and 11), an output is turned on.

OUTPUT ACTIVATION

For the input word 00, both the bits are inverted by NOT gates 1 & 2 and given to the AND gate 1. This AND gate 1 would go high thus making the corresponding output D0 as 1.

For the input word 01, the MSB bit is alone inverted by NOT gate 2  and given to the AND gate 2. The LSB is directly given to AND gate 2. The AND gate 2 would go high thus making the corresponding output D1 as 1.

For the input word 10, the LSB bit is alone inverted by NOT gate 1 and given to the AND gate 3. The MSB is directly given to AND gate 3. The AND gate 3 would go high thus making the corresponding output D2 as 1.

For the input word 11, both the bits are directly given to an AND gate 4. This AND gate 4 would go high thus making the corresponding output D3 as 1.

Also, read 
Difference between synchronous and asynchronous sequential circuits

Difference between combinational and sequential circuits