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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?
- a)7
- b)8
- c)9
- d)10
Correct answer is option 'C'. Can you explain this answer?
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Most Upvoted Answer
How many 3 × 8 line decoders with an enable input line are neede...
Concept:
Decoder expansion
n1 × m1 → n2 × m2
D1 D2
Number of D2 decoder required = ∑ K
⋮
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
Important Points
Decoder expansion
n1 × m1 → n2 × m2
D1 D2
Number of D2 decoder required = ∑ K
⋮
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
Important Points
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Community Answer
How many 3 × 8 line decoders with an enable input line are neede...
Understanding the Problem
To construct a 6 × 64 line decoder, we need to decode 6 input bits into 64 output lines. A 3 × 8 line decoder can decode 3 input bits into 8 output lines.
Breaking Down the Requirements
- Inputs: The 6 input lines can be divided into two groups.
- First Group: Utilize 3 bits for the first decoder.
- Second Group: Utilize 3 bits for the second decoder.
Using 3 × 8 Line Decoders
1. First Level Decoding:
- Use 1 decoder for the first 3 input bits.
- This decoder will provide 8 outputs, each corresponding to a unique combination of the first 3 bits.
2. Second Level Decoding:
- Each output of the first decoder can enable one of the 8 second decoders.
- Each of these second decoders will take the remaining 3 bits as input.
- Since there are 8 outputs from the first decoder, we need 8 second decoders.
Total Count of Decoders
- 1 decoder for the first level.
- 8 decoders for the second level.
Final Calculation
By summing the decoders:
- Total decoders = 1 (first level) + 8 (second level) = 9 decoders needed.
Thus, the correct answer is option C: 9.
This arrangement allows decoding of all 6 bits into 64 unique outputs using only 3 × 8 line decoders.
To construct a 6 × 64 line decoder, we need to decode 6 input bits into 64 output lines. A 3 × 8 line decoder can decode 3 input bits into 8 output lines.
Breaking Down the Requirements
- Inputs: The 6 input lines can be divided into two groups.
- First Group: Utilize 3 bits for the first decoder.
- Second Group: Utilize 3 bits for the second decoder.
Using 3 × 8 Line Decoders
1. First Level Decoding:
- Use 1 decoder for the first 3 input bits.
- This decoder will provide 8 outputs, each corresponding to a unique combination of the first 3 bits.
2. Second Level Decoding:
- Each output of the first decoder can enable one of the 8 second decoders.
- Each of these second decoders will take the remaining 3 bits as input.
- Since there are 8 outputs from the first decoder, we need 8 second decoders.
Total Count of Decoders
- 1 decoder for the first level.
- 8 decoders for the second level.
Final Calculation
By summing the decoders:
- Total decoders = 1 (first level) + 8 (second level) = 9 decoders needed.
Thus, the correct answer is option C: 9.
This arrangement allows decoding of all 6 bits into 64 unique outputs using only 3 × 8 line decoders.
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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?a)7b)8c)9d)10Correct answer is option 'C'. Can you explain this answer?
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