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Use a concrete representation on a place value chart to perform the following additions. (a) 11four + 13four

Use a concrete representation on a place value chart to perform the following additions. (a) 11four + 13four

Advanced Engineering Mathematics
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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**Exercise 8** Use a concrete representation on a place value chart to perform the following additions. (a) \( 11_{\text{four}} + 13_{\text{four}} \) --- **Explanation on Educational Website:** For this exercise, consider utilizing a place value chart for base four to solve the addition problem \( 11_{\text{four}} + 13_{\text{four}} \). Let's break down each number according to its place values in base four, which are similar to ones and fours (analogous to ones and tens in the decimal system). 1. **Number Representation:** - \( 11_{\text{four}} \) consists of: - 1 four - 1 one - \( 13_{\text{four}} \) consists of: - 1 four - 3 ones 2. **Addition in Base Four:** - Add the ones column: \( 1 + 3 = 4 \). - Since we are in base four, we convert 4 ones into 1 four and 0 ones. - Add the fours column with the carry-over: \( 1 + 1 + 1 = 3 \). **Result:** The sum is \( 30_{\text{four}} \). By visualizing this process on a place value chart, the understanding of base four addition becomes more manageable.
Transcribed Image Text:**Exercise 8** Use a concrete representation on a place value chart to perform the following additions. (a) \( 11_{\text{four}} + 13_{\text{four}} \) --- **Explanation on Educational Website:** For this exercise, consider utilizing a place value chart for base four to solve the addition problem \( 11_{\text{four}} + 13_{\text{four}} \). Let's break down each number according to its place values in base four, which are similar to ones and fours (analogous to ones and tens in the decimal system). 1. **Number Representation:** - \( 11_{\text{four}} \) consists of: - 1 four - 1 one - \( 13_{\text{four}} \) consists of: - 1 four - 3 ones 2. **Addition in Base Four:** - Add the ones column: \( 1 + 3 = 4 \). - Since we are in base four, we convert 4 ones into 1 four and 0 ones. - Add the fours column with the carry-over: \( 1 + 1 + 1 = 3 \). **Result:** The sum is \( 30_{\text{four}} \). By visualizing this process on a place value chart, the understanding of base four addition becomes more manageable.
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