##### Consider a pipelining with m stage and n instr...

Consider a pipelining with m stage and n instructions. The probabilities that a instruction will be conditional is 'p' and it will evaluates to be true is 'q'. What can be effective CPI ?

(A) 1+pq(n-1) | |

(B) 1+pq(m-1) | |

(C) 1+mpq(n-1) | |

(D) 1+npq(n-1) |

Total number of conditional branch instructions= np

Total number of instructions which actually branch = npq

Total number of instruction which will not branch = n-npq = n(1-pq)

Effective CPI = (m*npq+n(1-pq))/n

=mpq+(1-pq)

=1+pq(m-1)