Decoder

Decoder:

It is a combinational logic circuit which does opposite of Encoder. A decoder converts a binary number to its equivalent decimal or hexadecimal number.

Types of Decoder:

We will study following types of decoders:

        1)    2 to 4 Decoder        (2 inputs and 4 outputs)

        2)    3 to 8 Decoder        (3 inputs and 8 outputs)

        3)    4 to 16 Decoder        (4 inputs and 16 outputs)

2 to 4 Decoder:

Since 2 binary bits can store a maximum of 3 in decimal number system, thus a 2 to 4 decoder has 2 input lines which accepts 4 set of truth values and generates 4 decimal numbers (0 to 3) as output.

It can be represented by the following rule:
                    Number of Outputs = 2ⁿ, where n= Number of Inputs

     thus if inputs are 2, then output values are 2² i.e. 4,

similarly if inputs are 3, then output values are 2³ i.e. 8.

Truth Table for 2 to 4 Decoder:

Input		Output
x	y	D3	D2	D1	D0
0	0	0	0	0	1
0	1	0	0	1	0
1	0	0	1	0	0
1	1	1	0	0	0

In the above truth table the gate against the set of input values representing equivalent decimal number gets output value 1.
for example: when we pass values for input x & y as 1 & 0 respectively then gate D2 will get its value 1 against the input set as 10 is decimal equivalent of 2.

Logic Circuit & Block diagrams for 2 to 4 Decoder:

Here is the logic circuit and Block diagrams of a 2 to 4 Decoder:

Logic Circuit Diagram

Block Diagram

3 to 8 Decoder:

A 3 to 8 decoder has 3 input lines for binary number as input and it generates 8 decimal values as output.

Truth Table for 3 to 8 Decoder:

Input			Output
x	y	z	D7	D6	D5	D4	D3	D2	D1	D0
0	0	0	0	0	0	0	0	0	0	1
0	0	1	0	0	0	0	0	0	1	0
0	1	0	0	0	0	0	0	1	0	0
0	1	1	0	0	0	0	1	0	0	0
1	0	0	0	0	0	1	0	0	0	0
1	0	1	0	0	1	0	0	0	0	0
1	1	0	0	1	0	0	0	0	0	0
1	1	1	1	0	0	0	0	0	0	0

Logic Circuit & Block diagrams for 3 to 8 Decoder:

Here is the logic circuit and Block diagrams of a 3 to 8 Decoder:

Block Diagram

Logic Circuit Diagram