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The instruction ishl (shift left integer) exists in jvm but not in ijvm. it uses the top two values on the stack, replacing the two with a single value, the result. the sec- ond-from-top word of the stack is the operand to be shifted. its content is shifted left by a value between 0 and 31, inclusive, depending on the value of the 5 least signifi- cant bits of the top word on the stack (the other 27 bits of the top word are ignored). zeros are shifted in from the right for as many bits as the shift count. the opcode for ishl is 120 (0x78).a. what is the arithmetic operation equivalent to shifting left with a count of 2? b. extend the microcode to include this instruction as a part of ijv.

Suppose there is a relation r(a, b, c) with a b+-tree index with search keys (a, b).1. what is the worst-case cost of finding records satisfying 10 < a < 50 using this index, in terms of the number of records n1, retrieved and the height h of the tree? 2. what is the worst-case cost of finding records satisfying 10 < a < 50 and 5 < b < 10 using this index, in terms of the number of records n2 that satisfy this selection, as well as n1 and h defined above? 3. under what conditions on n1 and n2, would the index be an efficient way of finding records satisfying the condition from part (2)?

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