Question
Consider a computer that uses 5 bits to represent nonnegative integers and uses all 5 bits to represent the value.
Which of the following operations would result in integer overflow?
👁️Note that there may be multiple answers to this question.
Choose all answers that apply:
Choose all answers that apply:
(Choice A) \[18 + 14\]
A
\[18 + 14\]
(Choice B) \[8 \times 4\]
B
\[8 \times 4\]
(Choice C) \[15 + 1\]
C
\[15 + 1\]
(Choice D) \[8 + 4\]
D
\[8 + 4\]
(Choice E) \[12 \times 2\]
E
\[12 \times 2\]
(Choice F) \[12 + 2\]
F
\[12 + 2\]
Which of the following operations would result in integer overflow?
👁️Note that there may be multiple answers to this question.
Choose all answers that apply:
Choose all answers that apply:
(Choice A) \[18 + 14\]
A
\[18 + 14\]
(Choice B) \[8 \times 4\]
B
\[8 \times 4\]
(Choice C) \[15 + 1\]
C
\[15 + 1\]
(Choice D) \[8 + 4\]
D
\[8 + 4\]
(Choice E) \[12 \times 2\]
E
\[12 \times 2\]
(Choice F) \[12 + 2\]
F
\[12 + 2\]
Answers
GPT-4o mini
To determine which operations would result in integer overflow using 5 bits to represent nonnegative integers, we first need to understand the maximum value that can be represented with 5 bits. Since 5 bits can represent values from 0 to \(2^5 - 1\), the maximum value in this case is:
\[
2^5 - 1 = 32 - 1 = 31
\]
Now we will evaluate each operation and check if it results in a value greater than 31:
**Choice A: \(18 + 14\)**
\[
18 + 14 = 32
\]
This results in 32, which is not representable in 5 bits. **Overflow occurs.**
**Choice B: \(8 \times 4\)**
\[
8 \times 4 = 32
\]
This also results in 32, which is not representable in 5 bits. **Overflow occurs.**
**Choice C: \(15 + 1\)**
\[
15 + 1 = 16
\]
This is within the range (0 to 31). **No overflow.**
**Choice D: \(8 + 4\)**
\[
8 + 4 = 12
\]
This is within the range (0 to 31). **No overflow.**
**Choice E: \(12 \times 2\)**
\[
12 \times 2 = 24
\]
This is within the range (0 to 31). **No overflow.**
**Choice F: \(12 + 2\)**
\[
12 + 2 = 14
\]
This is within the range (0 to 31). **No overflow.**
In summary, the operations that would result in integer overflow are:
- **Choice A: \( 18 + 14 \)**
- **Choice B: \( 8 \times 4 \)**
So the correct answers are:
- A
- B
\[
2^5 - 1 = 32 - 1 = 31
\]
Now we will evaluate each operation and check if it results in a value greater than 31:
**Choice A: \(18 + 14\)**
\[
18 + 14 = 32
\]
This results in 32, which is not representable in 5 bits. **Overflow occurs.**
**Choice B: \(8 \times 4\)**
\[
8 \times 4 = 32
\]
This also results in 32, which is not representable in 5 bits. **Overflow occurs.**
**Choice C: \(15 + 1\)**
\[
15 + 1 = 16
\]
This is within the range (0 to 31). **No overflow.**
**Choice D: \(8 + 4\)**
\[
8 + 4 = 12
\]
This is within the range (0 to 31). **No overflow.**
**Choice E: \(12 \times 2\)**
\[
12 \times 2 = 24
\]
This is within the range (0 to 31). **No overflow.**
**Choice F: \(12 + 2\)**
\[
12 + 2 = 14
\]
This is within the range (0 to 31). **No overflow.**
In summary, the operations that would result in integer overflow are:
- **Choice A: \( 18 + 14 \)**
- **Choice B: \( 8 \times 4 \)**
So the correct answers are:
- A
- B