https://file.aiquickdraw.com/mathbot/file/1726017159511g23tjhs9.jpg

The image contains several arithmetic operations involving numbers in different bases (octal, hexadecimal, and binary). Here's a breakdown of each expression that needs to be solved:

1. **(3671)₈ + (4017)₈**  
   This is an addition in base 8 (octal).

2. **(50321)₈ - (67066)₈**  
   This is a subtraction in base 8 (octal).

3. **(A29F)₁₆ + (4798)₁₆**  
   This is an addition in base 16 (hexadecimal).

4. **(54AE9)₁₆ - (39F87)₁₆**  
   This is a subtraction in base 16 (hexadecimal).

5. **(11101011)₂ - (11001101)₂**  
   This is a subtraction in base 2 (binary).

I'll solve each of these step by step.

### Problem 1: \( (3671)_8 + (4017)_8 \)
I'll start by converting these numbers from base 8 to base 10, perform the addition in base 10, and then convert back to base 8.

### Problem 2: \( (50321)_8 - (67066)_8 \)
This involves similar steps: conversion from octal to decimal, subtraction in decimal, and conversion back to octal.

### Problem 3: \( (A29F)_{16} + (4798)_{16} \)
First, both hexadecimal numbers will be converted to decimal, added, and then converted back to hexadecimal.

### Problem 4: \( (54AE9)_{16} - (39F87)_{16} \)
This involves converting both hexadecimal numbers to decimal, subtracting, and converting back to hexadecimal.

### Problem 5: \( (11101011)_2 - (11001101)_2 \)
This binary subtraction will be done directly by converting the binary numbers to decimal, subtracting, and converting back to binary.

Let me perform these calculations for you.Here are the results for the problems from the image:

1. **(3671)₈ + (4017)₈ = (7710)₈**  
   The sum in octal is \( 7710_8 \).

2. **(50321)₈ - (67066)₈ = (-16545)₈**  
   The result is negative, written as \( -16545_8 \) (in octal).

3. **(A29F)₁₆ + (4798)₁₆ = (EA37)₁₆**  
   The sum in hexadecimal is \( EA37_{16} \).

4. **(54AE9)₁₆ - (39F87)₁₆ = (1AB62)₁₆**  
   The result in hexadecimal is \( 1AB62_{16} \).

5. **(11101011)₂ - (11001101)₂ = (11110)₂**  
   The result in binary is \( 11110_2 \).

Let me know if you'd like more details or further clarifications!

Here are some related questions:
1. How do you convert from one base to another without intermediate decimal conversion?
2. What are the rules for binary subtraction?
3. How is overflow handled in octal arithmetic?
4. Can you explain two's complement in binary for negative numbers?
5. What are some practical applications of hexadecimal arithmetic?

**Tip**: Always verify the final base of your result, especially when switching between different numbering systems.

Solve the following arithmetic operations in different bases:
1. (3671)₈ + (4017)₈
2. (50321)₈ - (67066)₈
3. (A29F)₁₆ + (4798)₁₆
4. (54AE9)₁₆ - (39F87)₁₆
5. (11101011)₂ - (11001101)₂

Learn how to solve arithmetic operations involving different number systems, including octal, hexadecimal, and binary. This tutorial covers step-by-step conversions and calculations, making it ideal for high school students.

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