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?
- A.
0
- B.
103
- C.
22
- D.
55
Attempted by 74 students.
Show answer & explanation
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.