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How many 3 × 8 decoders are required to Construct a 4 × 16 decoder?
Concept:
A decoder is a combinational circuit that converts n lines of input into 2n lines of output.
Decoder expansion
n_{1} × m_{1} → n_{2} × m_{2}
D_{1} D_{2}
m_{2}/m_{1}= K_{1}
K_{1}/m_{1 }= K_{2}
K_{2}/m_{1 }= K_{3}
Number of D2 decoder required is given as:
∑ K = K_{1} + K_{2} + K_{3} + 
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
A _________ is a multipleinput, multipleoutput logic circuit which converts coded inputs into coded outputs, where the input and output code are different.
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 multiinput and multioutput 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.
___________ converts binarycoded information to unique outputs such as decimal, octal digits, etc.
Decoder:
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:
In a decoder, if the input lines are 4 then number of maximum output lines will be:
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 2^{n} O/P
i.e., n ≤ 2^{n}
I / P O / P
For 4 input lines n = 4
Maximum output lines = 2^{4} = 16
How many 3 × 8 line decoders with an enable input line are needed to construct a 6 × 64 line decoder without using any other logic gate?
Concept:
Decoder expansion
n_{1 }× m_{1} → n_{2 }× m_{2}
D_{1} D_{2}
Number of D_{2} decoder required = ∑ K
m_{2} / m_{1} = K_{1}
K_{1} / m_{1} = K_{2}
K_{2} / m_{1} = K_{3}
⋮
Till 0 or 1
Calculation:
Given decoder 1 is 3 × 8 and the second decoder is 6 × 64
64 / 8 = 8
8 / 8 = 1
Number of 3 × 8 decoders = 8 + 1
Number of 3 × 8 decoders = 9
Direction: Given question consists of two statements, one labeled as the 'Assertion (A)' and the other as 'Reason (R)'. You are to examine these two statements carefully and select the answers to these items using the codes given below.
Assertion (A): A demultiplexer cannot be used as a decoder.
Reason (R): A demultiplexer selects one of many outputs, whereas a decoder selects an output corresponding to the coded input.
Decoder:
Generally, a decoder converts a binary number into any other format (decimal, hexadecimal, etc)
Eg: 2 × 4 decoder
Truth Table:
DeMUX: A demultiplexer takes a single input line and produces many output lines.
Now if we put input pin (I) of DeMUX remains at logic 1 and at select pin of DeMUX (S_{1}, S_{0}) we apply i / p (A, B) of decoder then DeMUX will be work as decoder. {I = 1}
Eg:
AB = 00 = S_{1} S_{0} ;
Y_{0} = 1 Y_{1} = 0 Y_{2} = 0 Y_{3} = 0
AB = 10 = S_{1} S_{0} ;
Y_{0} = 0 Y_{1} = 0 Y_{2} = 1 Y_{3} = 0
The number of input lines in a common BCD to seven segment decoder is _____.
Notes:
A 1 to 8 demultiplexer with data input D_{in}, address inputs S_{0}, S_{1}, and S_{2}, (with S_{0} as the LSB) and Y̅_{0} to Y̅ _{7} as the eight demultiplexed output, is to be designed using two 2 to 4 decoders (with enable input E and address input A_{0} and A_{1}) as shown in the figure. D_{in}, S_{0}, S_{1}, and S_{2} are to be connected to P, Q, R, and S but not necessarily in this order. The respective input connections to P, Q, R, and S terminals should be
The given question is the expansion of
2 : 4 decoder to 1 : 8 decoder
We need to implement 1 : 8 DEMUX.
So, select lines of DeMux should be mapped to address lines of the decoder.
The LSB of DeMux should be connected to the LSB of address lines of the decoder
∴ R → S0
and S→ S_{1}
Input to both the decoder should be same so
∴ P → D_{in}
∴ NOT gate along with OR gate in case to select one decoder at a time so Q → S_{2}
So,
P → Din
Q → S2
R → S_{0 }
S→ S1
Hence option (D) is correct
Find the number of 2 × 1 MUX (multiplexers) required to implement 16 × 1 MUX.
To implement 2^{n} × 1 MUX using 2 × 1 MUX, the total number of 2 × 1 MUX required is (2^{n}  1).
∴ The number of 2 × 1 multiplexer required to implement 16 × 1 MUX will be:
n = 16  1 = 15
Or we can follow the below steps to calculate the same:
1^{st} stage = 16/2 = 8
2^{nd} stage = 8/2 = 4
3^{rd} stage = 4/2 = 2
4^{th }stage = 2/2 = 1
The sum will give the total number of MUX required to implement 16 × 1 multiplexer using 2 × 1, i.e.
n = 8 + 4 + 2 + 1 = 15
Combinational circuit in which output depends only on the state of inputs.
Decoder circuits are constructed from Inverters and AND gates.
8870 is a DTMF decoder circuit, which decodes DTMF tune and produces corresponding output.
Decoder is a circuit with n input lines and 2^{n} output lines.
BCD to seven segment code conversion can be treated as a decoding process.
Which of the following represents a number of output lines for a decoder with 4 input lines?
For n input lined decoder will have 2^{n} output lines.
22 docs274 tests

22 docs274 tests
