Question
A binary number is to be transformed by appending three 0s to the end of the number. For example, 11101 is transformed to 11101000.
Question
31
Mark for Review
Which of the following correctly describes the relationship between the transformed number and the original number?
The transformed number is 3 times the value of the original number.
Option A,The transformed number is 3 times the value of the original number.
The transformed number is 4 times the value of the original number.
Option B,The transformed number is 4 times the value of the original number.
The transformed number is 8 times the value of the original number.
Option C,The transformed number is 8 times the value of the original number.
The transformed number is 1,000 times the value of the original number.
Question
31
Mark for Review
Which of the following correctly describes the relationship between the transformed number and the original number?
The transformed number is 3 times the value of the original number.
Option A,The transformed number is 3 times the value of the original number.
The transformed number is 4 times the value of the original number.
Option B,The transformed number is 4 times the value of the original number.
The transformed number is 8 times the value of the original number.
Option C,The transformed number is 8 times the value of the original number.
The transformed number is 1,000 times the value of the original number.
Answers
GPT-4o mini
To determine the relationship between the transformed binary number and the original binary number, we need to understand how appending zeros affects the value of a binary number.
When we append three zeros to the end of a binary number, we are effectively multiplying that number by \(2^3\) (which is 8), because each zero represents a shift in the binary place value.
Let's analyze it step by step:
1. **Understand the original number in binary:**
- Let’s say the original binary number is represented as \(N\).
2. **Transforming the number by appending three zeros:**
- Appending three zeros to \(N\) (in binary) results in the new binary number \(N000\).
3. **Calculating the value:**
- The value of the original number \(N\) in decimal represents whatever value \(N\) holds.
- The transformed number \(N000\) in binary effectively shifts \(N\) left by three places.
4. **Mathematical expression:**
- The new value can be expressed as:
\[
\text{Transformed value} = N \times 2^3 = N \times 8
\]
Based on this analysis, we can conclude that:
**The transformed number is 8 times the value of the original number.**
Thus, the correct answer is **Option C: The transformed number is 8 times the value of the original number.**
When we append three zeros to the end of a binary number, we are effectively multiplying that number by \(2^3\) (which is 8), because each zero represents a shift in the binary place value.
Let's analyze it step by step:
1. **Understand the original number in binary:**
- Let’s say the original binary number is represented as \(N\).
2. **Transforming the number by appending three zeros:**
- Appending three zeros to \(N\) (in binary) results in the new binary number \(N000\).
3. **Calculating the value:**
- The value of the original number \(N\) in decimal represents whatever value \(N\) holds.
- The transformed number \(N000\) in binary effectively shifts \(N\) left by three places.
4. **Mathematical expression:**
- The new value can be expressed as:
\[
\text{Transformed value} = N \times 2^3 = N \times 8
\]
Based on this analysis, we can conclude that:
**The transformed number is 8 times the value of the original number.**
Thus, the correct answer is **Option C: The transformed number is 8 times the value of the original number.**