Write the number as a binary number. 1228 122g =D2
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question
Write the number as a binary number.
![**Task: Convert an Octal Number to a Binary Number**
Consider the octal number: \(122_8\).
To convert the octal number \(122_8\) to a binary number, follow these steps:
1. **Write the Octal Number**:
\[
122_8
\]
2. **Convert Octal to Binary**:
Each octal digit corresponds to a three-digit binary number. Convert each digit individually.
- \(1_8\) in binary is \(001_2\)
- \(2_8\) in binary is \(010_2\)
- \(2_8\) in binary is \(010_2\)
Therefore, the binary equivalent is obtained by combining these binary groups.
\[
122_8 = 001\, 010\, 010_2
\]
Hence, the number \(122_8\) in binary is:
\[
122_8 = \boxed{001010010}_2
\]
**Summary**: The task requires converting the octal number \(122_8\) into its binary equivalent, which is \(001010010_2\).
This conversion is essential for understanding different numeral systems in computer science and digital electronics.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F105fff1d-4db1-4cc6-9fff-4ea0e94f4214%2Ff0ef65ce-6eb3-4c9b-84ce-249b94c6beb9%2F74nqaun_processed.png&w=3840&q=75)
Transcribed Image Text:**Task: Convert an Octal Number to a Binary Number**
Consider the octal number: \(122_8\).
To convert the octal number \(122_8\) to a binary number, follow these steps:
1. **Write the Octal Number**:
\[
122_8
\]
2. **Convert Octal to Binary**:
Each octal digit corresponds to a three-digit binary number. Convert each digit individually.
- \(1_8\) in binary is \(001_2\)
- \(2_8\) in binary is \(010_2\)
- \(2_8\) in binary is \(010_2\)
Therefore, the binary equivalent is obtained by combining these binary groups.
\[
122_8 = 001\, 010\, 010_2
\]
Hence, the number \(122_8\) in binary is:
\[
122_8 = \boxed{001010010}_2
\]
**Summary**: The task requires converting the octal number \(122_8\) into its binary equivalent, which is \(001010010_2\).
This conversion is essential for understanding different numeral systems in computer science and digital electronics.
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