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Question

Number of 3*8 Decoders required to construct a 9×2⁹ Decoder having 3 levels.

Comments

1+8+64 = 73 decoders.

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Either calculate by intuition,

Lvl 1 : such as I₈I₇I₆ given for one decoder at 1st level, which will give 8 outputs,

Lvl 2 :Then use 8 outputs as enable of new 8 decoders each has inputs I₅I₄I₃

Lvl  3 : Then use 8 outputs of each decoder = 64 outputs as enable of newly 64 decoders. each has input I₂I₁I₀

Or use formula $\sum_{k=1}^{log m base n} \left ( \frac{m}{n^k} \right )$

where n = 8 m = 2^9

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thanks