Test: Decoders - GATE MCQ

Concept:

 A decoder is a combinational circuit that converts n lines of input into 2n lines of output.

Decoder expansion

n₁ × m₁ → n₂ × m₂

Number of D₂ decoder required is given as:

∑ K = K₁ + K₂ + K₃ + ------ 

Calculation:

Given decoder 1 is 3 × 8 and the second decoder is 4 × 16

16/8 = 2

2/8 = 0

Number of 3 × 8 decoders = 2 + 0

Number of 3 × 8 decoders = 2

The implementation is shown below.

Encoder:

An encoder has 2n input lines and n output lines. In the encoder, the output lines generate the binary code corresponding to the input value which is active high.

Decoder:

It is a multi-input and multi-output logic circuit that converts coded inputs into coded outputs where input and output codes are different. Input code has fewer bits than output code. There is one to one mapping from input to output.

Multiplexer:

It is a digital switch. It allows digital information from several sources to be routed onto a single output line. A basic multiplexer has several data input lines and a single output line. The selection of a particular input line is controlled by selection lines. It is many to one mapping and provides the digital equivalent of an analog selector switch. Therefore it is the correct answer

Demultiplexer:

It is a circuit that receives information on a single line and transmits information on one of the 2n output lines. Selection of output line is controlled by values of n selection lines. 

Decoder:

• A decoder is a combinational circuit that has ‘n’ input lines and a maximum of 2n output lines.
• Decoder converts binary-coded information to unique outputs such as decimal, octal digits, etc.
• A particular output will be active High depending upon the combination of inputs present when the decoder is enabled.
• We can, therefore, conclude that a decoder detects a particular code.

A 2 to 4 decoder is shown in the block diagram below:

Truth Table:

Application:

A decoder is used to convert a BCD code to a 7 segment code. This is explained in the following block diagram:

Decoder:

The decoder is a combinational ckt, that convert Binary Coded information into Familiar, representation like the decimal, octal, Hexadecimal, etc.

The decoder has ‘n’ no of i/p & less than equal to 2n O/P

For 4 input lines n = 4

Maximum output lines = 2⁴ = 16

Concept:

The simple decoder is shown below:

Addressing is done based on the inputs and their respective logic circuit connected to the address decoders.

Calculation:

In the given question the chip select for Y5 is 101.

A₁₀A₉A₈ are used for that chip select so A₁₀A₉A₈ = 101.

A₇ ⋯ A₀ are initially zeroes and at the final address these will be all 1’s.

To get the active high output for the NAND gate all the inputs must be 1 always.

The total addressing range is shown below:

FD00H to FDFFH

A is false but R is true. A demultiplexer can be used as a decoder.

Decoder:

Generally, a decoder converts a binary number into any other format (decimal, hexadecimal, etc)

Eg: 2 × 4 decoder

Truth table:

Eg:

AB = 00 = S₁ S₀ ;

Y₀ = 1 Y₁ = 0 Y₂ = 0 Y₃ = 0

AB = 10 = S₁ S₀ ;

Y₀ = 0 Y₁ = 0 Y₂ = 1 Y₃ = 0

• In BCD to 7-segment Decoder, the outputs of a digital circuit are often displayed as decimal digits.
• BCD to 7-segment decoder is a combinational circuit that converts a BCD number into signals that are required for the display of the value of that number on a seven-segment display.
• The number of input lines is 4. 

Decoder is a circuit with n input lines and 2ⁿ output lines.

Decoder circuits are constructed from Inverters and AND gates.

For n input lined decoder will have 2ⁿ output lines.