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A digital computer has a common bus system for 16 registers of 32 bits each. The bus is constructed
with multiplexers.

[i] How many selection inputs are there in each multiplexer?
[ii] What size of multiplexers is needed?
[iii] How many multiplexers are there in the bus?

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According to formua if there are N number of K bit register,then there should be K number of NX1 Mux

so according to your question

2)16X1 sized multiplexer needed

3)32 multiplexers are there in bus

1)4 selection input are there in the multiplexer

correct me if i am wrong   MORRIS MANO PAGE 99
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ok sir you are right thank you sir :)
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can you kindly explain why would it be 32 multiplexers in the bus?
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The size of a multiplexer is decide based on the number of data inputs it needs to handle.It is given in the question that there are 16 registers each of size 32 bits and in a common bus system using multiplexers, each multiplexer takes one input from every register. So, to take one input form 32 registers, we need 32 multiplexers to select each single input from the given 16 registers of size 32 bits each.

I hope this clears up your doubt.
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