Consider a computer that uses 5 bits to represent integers, using 1 bit for
the sign and 4 bits for the actual value.
Which of the following operations would result in integer overflow?
Note that there are 2 answers to this question.
Choose 2 answers:
A 7+1
B
12 +3
C
6 + 9
D
8 x 2
E
2 X 4
F
1 + 15

Question

Accepted Answer

∻Explanation∻ ⚹Integer overflow occurs when an arithmetic operation results in a value that exceeds the maximum or minimum value that can be represented within the given number of bits. In this case, the computer uses 5 bits to represent integers, with 1 bit for the sign and 4 bits for the actual value.⚹ ∻Step-by-step Instruction∻ ‖ ▪ ⋮ Determine the range of integers that can be represented with 5 bits (1 bit for sign and 4 bits for value). ‖ ‖ ▪ ⋮ The range is from -8 to 7. ‖ ‖ ▪ ⋮ Evaluate each operation to see if the result falls outside this range. ‖ ‖ ▪ ⋮ Identify the operations that result in values outside the range of -8 to 7. ‖ Let's evaluate each operation: 1. **7 + 1** - 7 + 1 = 8 - 8 is outside the range of -8 to 7. - **This results in integer overflow.** 2. **12 + 3** - 12 + 3 = 15 - 15 is outside the range of -8 to 7. - **This results in integer overflow.** 3. **6 + 9** - 6 + 9 = 15 - 15 is outside the range of -8 to 7. - **This results in integer overflow.** 4. **8 x 2** - 8 * 2 = 16 - 16 is outside the range of -8 to 7. - **This results in integer overflow.** 5. **2 x 4** - 2 * 4 = 8 - 8 is outside the range of -8 to 7. - **This results in integer overflow.** 6. **1 + 15** - 1 + 15 = 16 - 16 is outside the range of -8 to 7. - **This results in integer overflow.** ∻Time Complexity∻ ⚹The time complexity for evaluating each operation is O(1) since each arithmetic operation is a constant-time operation.⚹ ∻Space Complexity∻ ⚹The space complexity is O(1) as no additional space is required beyond the input values.⚹ Based on the above evaluation, the operations that result in integer overflow are: - **7 + 1** - **12 + 3**

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