Write each binary number first as an octal number and then as a hexadecimal number. 10111000112
Write each binary number first as an octal number and then as a hexadecimal number. 10111000112
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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Write each binary number first as an octal number and then as a hexadecimal number.
1011100011_2
![### Binary to Octal and Hexadecimal Conversion
**Problem Statement:**
Convert the given binary number into both octal and hexadecimal formats.
**Binary Number:**
\[ 1011100011_2 \]
**Steps for Conversion:**
1. **Binary to Octal:**
- Split the binary number into groups of three digits starting from the right.
- Convert each group of three binary digits into its octal equivalent.
Example Conversion:
- Binary: 1011100011
- Split into groups of three: (001)(011)(100)(011)
- Convert each group:
- \(001_2\) = \(1_8\)
- \(011_2\) = \(3_8\)
- \(100_2\) = \(4_8\)
- \(011_2\) = \(3_8\)
- Octal Number: \(1343_8\)
2. **Binary to Hexadecimal:**
- Split the binary number into groups of four digits starting from the right.
- Convert each group of four binary digits into its hexadecimal equivalent.
Example Conversion:
- Binary: 1011100011
- Split into groups of four: (0001)(0111)(0011)
- Convert each group:
- \(0001_2\) = \(1_{16}\)
- \(0111_2\) = \(7_{16}\)
- \(1011_2\) = \(B_{16}\)
- Hexadecimal Number: \(17B_{16}\)
By following these steps, you can convert the given binary number into its respective octal and hexadecimal forms.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F105fff1d-4db1-4cc6-9fff-4ea0e94f4214%2F342802de-3175-4c89-9988-835783868976%2Faf0e65_processed.png&w=3840&q=75)
Transcribed Image Text:### Binary to Octal and Hexadecimal Conversion
**Problem Statement:**
Convert the given binary number into both octal and hexadecimal formats.
**Binary Number:**
\[ 1011100011_2 \]
**Steps for Conversion:**
1. **Binary to Octal:**
- Split the binary number into groups of three digits starting from the right.
- Convert each group of three binary digits into its octal equivalent.
Example Conversion:
- Binary: 1011100011
- Split into groups of three: (001)(011)(100)(011)
- Convert each group:
- \(001_2\) = \(1_8\)
- \(011_2\) = \(3_8\)
- \(100_2\) = \(4_8\)
- \(011_2\) = \(3_8\)
- Octal Number: \(1343_8\)
2. **Binary to Hexadecimal:**
- Split the binary number into groups of four digits starting from the right.
- Convert each group of four binary digits into its hexadecimal equivalent.
Example Conversion:
- Binary: 1011100011
- Split into groups of four: (0001)(0111)(0011)
- Convert each group:
- \(0001_2\) = \(1_{16}\)
- \(0111_2\) = \(7_{16}\)
- \(1011_2\) = \(B_{16}\)
- Hexadecimal Number: \(17B_{16}\)
By following these steps, you can convert the given binary number into its respective octal and hexadecimal forms.
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