### Understanding a Base-4 Place-Value SystemIn this example, we will learn how to interpret and convert numbers from a base-4 place-value system to the more familiar base-10 system.#### Base-4 System Representation:The digits in the base-4 system are represented by the following symbols:- $ \textcolor{blue}{B} $ = 0- $ \textcolor{red}{R} $ = 1- $ \textcolor{orange}{O} $ = 2- $ \textcolor{green}{G} $ = 3### Exercises**a. Determine the value of $ \textcolor{red}{R} \textcolor{green}{G} \textcolor{blue}{B} \textcolor{red}{R} \textcolor{green}{G} $ in base 10.**In this step, convert the given base-4 number $ \textcolor{red}{R} \textcolor{green}{G} \textcolor{blue}{B} \textcolor{red}{R} \textcolor{green}{G} $ to base 10.**b. Write 180 in the base-4 system using only the symbols shown to the right.**Convert the base-10 number 180 to the base-4 system using the symbols $ \textcolor{blue}{B} $, $ \textcolor{red}{R} $, $ \textcolor{orange}{O} $, and $ \textcolor{green}{G} $.#### Solution for Part (a):The value of $ \textcolor{red}{R} \textcolor{green}{G} \textcolor{blue}{B} \textcolor{red}{R} \textcolor{green}{G}_4 $ in base 10 is _.\[ \boxed{\text{Simplify your answer.}} \]

In the decimal number system, the place value of each digit is represented in terms of 10n . For…

Suppose a base 4 place-value system has its digits represented as shown to the right. a. Determine the value of RGBRG, in base 10. b. Write 180 in the base 4 system using only the symbols shown to the right. a. The value of RGBRG¸ in base 10 is (Simplify your answer.)

Suppose a base 4 place-value system has its digits represented as shown to the right. a. Determine the value of RGBRG, in base 10. b. Write 180 in the base 4 system using only the symbols shown to the right. a. The value of RGBRG¸ in base 10 is (Simplify your answer.)

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

### Understanding a Base-4 Place-Value System

In this example, we will learn how to interpret and convert numbers from a base-4 place-value system to the more familiar base-10 system.

#### Base-4 System Representation:

The digits in the base-4 system are represented by the following symbols:
- $ \textcolor{blue}{B} $ = 0
- $ \textcolor{red}{R} $ = 1
- $ \textcolor{orange}{O} $ = 2
- $ \textcolor{green}{G} $ = 3

### Exercises

**a. Determine the value of $ \textcolor{red}{R} \textcolor{green}{G} \textcolor{blue}{B} \textcolor{red}{R} \textcolor{green}{G} $ in base 10.**

In this step, convert the given base-4 number $ \textcolor{red}{R} \textcolor{green}{G} \textcolor{blue}{B} \textcolor{red}{R} \textcolor{green}{G} $ to base 10.

**b. Write 180 in the base-4 system using only the symbols shown to the right.**

Convert the base-10 number 180 to the base-4 system using the symbols $ \textcolor{blue}{B} $, $ \textcolor{red}{R} $, $ \textcolor{orange}{O} $, and $ \textcolor{green}{G} $.

#### Solution for Part (a):

The value of $ \textcolor{red}{R} \textcolor{green}{G} \textcolor{blue}{B} \textcolor{red}{R} \textcolor{green}{G}_4 $ in base 10 is _.

\[ \boxed{\text{Simplify your answer.}} \]

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