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+14 votes

How many 3-to-8 line decoders with an enable input are needed to construct a 6-to-64 line decoder without using any other logic gates?

  1. 7
  2. 8
  3. 9
  4. 10
asked in Digital Logic by Veteran (59.4k points) | 5.1k views
@Arjun Sir, please help to solve these type of questions.

4 Answers

+24 votes
Best answer
ans is C:

to get 6:64 we need 64 o/p

we have 3:8 decode with 8 o/p. so we need 64/8=8 decoders

now to select any of this 8 decoder we need one more decoder.

total=8+1= 9 decoders
answered by Loyal (8.3k points)
selected by
But then it should be called 3-64 decoder where is the six ??
When the first decoder will select any one of the 8 decoders attached with their enable lines  then rest of the decoder will not be counted and first decoder will have 3 inputs leaving enable line and the second decoder will have remaining 3 line hence, 6 inputs
Please explain with a diagram

If still not clear, here's the diagram just for you :)


Correct as the output depends on 6 inputs
I0, I1, I2 are most significant bits( input sequence- I0 I1 I2 I3 I4 I5 )
+15 votes

Answer : C

In first Level we need 64 / 8 = 8 Decoder

In second Level to cover 8 select lines Which are coming out from 8 decoder we need  8 / 8 = 1 Decoder

Total =8+1= 9 decoders

answered by Boss (45.1k points)
Can someone explain what I have written wrong in this Answer .I have got a downvote on it .Whoever gave it (downvote) please explain the correct method to solve it along with answer...
I think Ur not wrong
+8 votes

Quickest way to solve this type of problems will b:

Number of m bit MUX/DeMUX/Decoder/Encoder to construct N bit  MUX/DeMUX/Decoder/Encoder is:

ceil (N-1)/(M-1)

In given problem,  (N-1)/(M-1)= 64-1/8-1 =63/7 =9

answered by Boss (33.8k points)
Is this formula really true. Where does it come from, give some reference man.
–10 votes
ans 10
answered by Active (5.2k points)
a simple way of doing these type of question

just pick up maximum values from from both given and want to design.

in above question:

given  3-to-8

design 6-to-64

therefore 8 and 64


divide (64/8)=8

again till we reaached 1 or less then 1


then add both of them 8+1=9 your answer..

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