Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
expand_more
expand_more
format_list_bulleted
Related questions
Question
![**Convert the Numeral to a Numeral in Base 10**
**Given: \( B83_{12} \)**
To convert the numeral \( B83_{12} \) to a base 10 numeral, follow these steps:
1. **Understand the Base 12 System:**
- In base 12, the digits range from 0 to B, where A represents 10 and B represents 11 in base 10.
2. **Break Down the Numeral:**
- The numeral \( B83_{12} \) consists of the digits B, 8, and 3.
3. **Convert Each Digit:**
- Convert B to 11 in base 10.
- 8 remains 8 in base 10.
- 3 remains 3 in base 10.
4. **Calculate the Base 10 Value:**
- Multiply each digit by 12 raised to the power of its position, starting from right (position 0):
\[
B83_{12} = (11 \times 12^2) + (8 \times 12^1) + (3 \times 12^0)
\]
- Calculate each term:
- \( 11 \times 12^2 = 11 \times 144 = 1584 \)
- \( 8 \times 12^1 = 8 \times 12 = 96 \)
- \( 3 \times 12^0 = 3 \times 1 = 3 \)
5. **Sum the Values:**
\[
1584 + 96 + 3 = 1683
\]
Therefore, \( B83_{12} \) is \( 1683 \) in base 10.](https://content.bartleby.com/qna-images/question/6727d57a-eab8-4a5b-bd1a-5eddc663e9c0/34a11af0-fbf4-4a62-b161-1b3a123063ce/zuzaixo_processed.png)
Transcribed Image Text:**Convert the Numeral to a Numeral in Base 10**
**Given: \( B83_{12} \)**
To convert the numeral \( B83_{12} \) to a base 10 numeral, follow these steps:
1. **Understand the Base 12 System:**
- In base 12, the digits range from 0 to B, where A represents 10 and B represents 11 in base 10.
2. **Break Down the Numeral:**
- The numeral \( B83_{12} \) consists of the digits B, 8, and 3.
3. **Convert Each Digit:**
- Convert B to 11 in base 10.
- 8 remains 8 in base 10.
- 3 remains 3 in base 10.
4. **Calculate the Base 10 Value:**
- Multiply each digit by 12 raised to the power of its position, starting from right (position 0):
\[
B83_{12} = (11 \times 12^2) + (8 \times 12^1) + (3 \times 12^0)
\]
- Calculate each term:
- \( 11 \times 12^2 = 11 \times 144 = 1584 \)
- \( 8 \times 12^1 = 8 \times 12 = 96 \)
- \( 3 \times 12^0 = 3 \times 1 = 3 \)
5. **Sum the Values:**
\[
1584 + 96 + 3 = 1683
\]
Therefore, \( B83_{12} \) is \( 1683 \) in base 10.
Expert Solution
arrow_forward
Step 1: We write what we have to find out and given
Convert the numeral to a numeral in base 10.
B8312
Step by stepSolved in 3 steps with 1 images
Knowledge Booster
Similar questions
arrow_back_ios
arrow_forward_ios
Recommended textbooks for you
- Advanced Engineering MathematicsAdvanced MathISBN:9780470458365Author:Erwin KreyszigPublisher:Wiley, John & Sons, Incorporated
Numerical Methods for EngineersAdvanced MathISBN:9780073397924Author:Steven C. Chapra Dr., Raymond P. CanalePublisher:McGraw-Hill Education
Introductory Mathematics for Engineering Applicat...Advanced MathISBN:9781118141809Author:Nathan KlingbeilPublisher:WILEY 
Mathematics For Machine TechnologyAdvanced MathISBN:9781337798310Author:Peterson, John.Publisher:Cengage Learning,
Advanced Engineering Mathematics
Advanced Math
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:9780073397924
Author:Steven C. Chapra Dr., Raymond P. Canale
Publisher:McGraw-Hill Education
Introductory Mathematics for Engineering Applicat...
Advanced Math
ISBN:9781118141809
Author:Nathan Klingbeil
Publisher:WILEY
Mathematics For Machine Technology
Advanced Math
ISBN:9781337798310
Author:Peterson, John.
Publisher:Cengage Learning,