n instruction set of a processor has 125 signals which can be divided into 5…

2005

n instruction set of a processor has 125 signals which can be divided into 5 groups of mutually exclusive signals as follows:

Group 1 : 20 signals, Group 2 : 70 signals, Group 3 : 2 signals, Group 4 : 10 signals, Group 5 : 23 signals.

How many bits of the control words can be saved by using vertical microprogramming over horizontal microprogramming?

  1. A.

    0

  2. B.

    103

  3. C.

    22

  4. D.

    55

Attempted by 74 students.

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Correct answer: B

Key idea: use one control line per signal for horizontal microprogramming; vertical microprogramming encodes mutually exclusive groups.

Horizontal microprogramming bits:

  • Total signals = 125, so horizontal control word needs 125 bits.

Vertical microprogramming bits (encode each mutually exclusive group):

  • Group with 20 signals: ceil(log2(20)) = 5 bits

  • Group with 70 signals: ceil(log2(70)) = 7 bits

  • Group with 2 signals: ceil(log2(2)) = 1 bit

  • Group with 10 signals: ceil(log2(10)) = 4 bits

  • Group with 23 signals: ceil(log2(23)) = 5 bits

Total vertical bits = 5 + 7 + 1 + 4 + 5 = 22 bits.

Bits saved by using vertical over horizontal = 125 - 22 = 103 bits.

Answer: 103 bits can be saved.

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