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Consider the expression (a-1) * ((( b + c ) / 3 )) + d)). Let X be the minimum number of registers required by an optimal code generation (without any register spill) algorithm for a load/store architecture, in which
(i) only load and store instructions can have memory operands and
(ii) arithmetic instructions can have only register or immediate operands.
The value of X is ________.
Note: This questions appeared as Numerical Answer Type.
(i) only load and store instructions can have memory operands and
(ii) arithmetic instructions can have only register or immediate operands.
The value of X is ________.
Note: This questions appeared as Numerical Answer Type.
- a)2
- b)1
- c)4
- d)3
Correct answer is option 'A'. Can you explain this answer?
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Consider the expression (a-1) * ((( b + c ) / 3 )) + d)). Let X be the...
The assembly code using the load/store architecture can be written as follows:
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Consider the expression (a-1) * ((( b + c ) / 3 )) + d)). Let X be the...
Solution:
Given expression: (a-1) * ((( b c ) / 3 )) d))
We need to find the minimum number of registers required by an optimal code generation algorithm for a load/store architecture.
The expression consists of four variables a, b, c, and d, and two constants 1 and 3.
To minimize the number of registers required, we need to evaluate the expression in a way that minimizes the use of memory operands and maximizes the use of registers.
Let's analyze the expression:
1. (a-1) can be evaluated using one register and one memory operand.
2. (( b c ) / 3 ) can be evaluated using two registers and two memory operands.
3. The final result can be stored in one register.
Therefore, we need a total of 2 + 2 + 1 = 5 registers to evaluate the expression without any register spill.
However, the question states that we can only use load and store instructions for memory operands and arithmetic instructions can only have register or immediate operands.
This means that we cannot use memory operands directly in arithmetic instructions, and we need to load them into registers first.
To minimize the number of registers required, we can reuse the same registers for different memory operands.
Let's optimize the expression:
1. Load a into a register.
2. Subtract 1 from the register.
3. Load b into a register.
4. Load c into another register.
5. Multiply the two registers using a third register.
6. Load 3 into a register.
7. Divide the result in step 5 by the register in step 6 using a fourth register.
8. Load d into a fifth register.
9. Multiply the result in step 7 by the register in step 8 using a sixth register.
10. The final result is stored in the sixth register.
Therefore, we need a total of 6 registers to evaluate the expression without any register spill.
Hence, the correct answer is option A (2).
Given expression: (a-1) * ((( b c ) / 3 )) d))
We need to find the minimum number of registers required by an optimal code generation algorithm for a load/store architecture.
The expression consists of four variables a, b, c, and d, and two constants 1 and 3.
To minimize the number of registers required, we need to evaluate the expression in a way that minimizes the use of memory operands and maximizes the use of registers.
Let's analyze the expression:
1. (a-1) can be evaluated using one register and one memory operand.
2. (( b c ) / 3 ) can be evaluated using two registers and two memory operands.
3. The final result can be stored in one register.
Therefore, we need a total of 2 + 2 + 1 = 5 registers to evaluate the expression without any register spill.
However, the question states that we can only use load and store instructions for memory operands and arithmetic instructions can only have register or immediate operands.
This means that we cannot use memory operands directly in arithmetic instructions, and we need to load them into registers first.
To minimize the number of registers required, we can reuse the same registers for different memory operands.
Let's optimize the expression:
1. Load a into a register.
2. Subtract 1 from the register.
3. Load b into a register.
4. Load c into another register.
5. Multiply the two registers using a third register.
6. Load 3 into a register.
7. Divide the result in step 5 by the register in step 6 using a fourth register.
8. Load d into a fifth register.
9. Multiply the result in step 7 by the register in step 8 using a sixth register.
10. The final result is stored in the sixth register.
Therefore, we need a total of 6 registers to evaluate the expression without any register spill.
Hence, the correct answer is option A (2).
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Consider the expression (a-1) * ((( b + c ) / 3 )) + d)). Let X be the minimum number of registers required by an optimal code generation (without any register spill) algorithm for a load/store architecture, in which(i) only load and store instructions can have memory operandsand(ii) arithmetic instructions can have only register or immediate operands.The value of X is ________.Note:This questions appeared as Numerical Answer Type.a)2b)1c)4d)3Correct answer is option 'A'. Can you explain this answer?
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