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A micro program control unit is required to generate a total of 25 control signals. Assume that
during any micro instruction, at most two control signals are active. The number of bits
required in the control word to generate the required control signals will be:

(I changed a previous year gate question. In this question  I am asking about horizontal microprogramming)

If u want to solve it using horizontal programming than the question should not include "at most two " word because in horizontal programming u can use all signals.

But if u want to have at most two signals  then vertical programming is required.
Which means in horizontal microprogramming we need 25 bits ?
In horizontal programming each bit represent a signal. Total we have 25 signals and for them we need 25 bits.

10 Bits

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In horizontal micro programming each bit represents a signal.

Total control signals are 25 therefore no of bits = 25
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I don’t for sure, but I think in this way. Say you have 25 control signals out of which any 2 will be working at a time, then in no of ways we use 2 signals at a time is 25C2 = 300. So we need to handle this 300 conditions for which 9 bits would be required