✅ Step 1: Convert Octal to Binary

Each octal digit is represented by 3 binary digits. Let's convert (2217)₈ to binary:

2₈ = 010, 2₈ = 010, 1₈ = 001, 7₈ = 111

Binary Representation: 010 010 001 111

✅ Step 2: Group Binary in 4-bit Sections

To convert binary to hexadecimal, group the binary digits in sets of 4, starting from the right:

010 010 001 111 becomes 0010 0100 0111

✅ Step 3: Convert Binary to Hexadecimal

Now convert each group of 4 bits into its hexadecimal equivalent:

• 0010 = 2
• 0100 = 4
• 0111 = 7

✅ Final Answer:

The hexadecimal equivalent of (2217)₈ is: (247)16

✅ Concept:

Binary multiplication is done similarly to decimal multiplication, where each bit is multiplied individually. Let's break down $00_2 \times 11_2$ step by step.

✅ Step 1: Understanding Binary Multiplication

We multiply each digit in the first binary number by each digit in the second binary number. The multiplication follows the same rules as decimal multiplication but with only 0's and 1's.

✅ Step 2: Perform the Multiplication

Let's multiply the two binary numbers:

• First step: $0 \times 1 = 0$
• Second step: $0 \times 1 = 0$
• Third step: $0 \times 1 = 0$

✅ Step 3: Adding the Results

Since all the results are 0, the final multiplication result is also 0.

✅ Final Answer:

The result of $00_2 \times 11_2$ is: 0

Decimal to Binary Conversion

? Given: Convert (25.375)10 to binary.

? Step-by-step:

• Integer Part (25):
  Divide by 2 repeatedly:

  25 ÷ 2 = 12 remainder 1  
  12 ÷ 2 = 6  remainder 0  
  6  ÷ 2 = 3  remainder 0  
  3  ÷ 2 = 1  remainder 1  
  1  ÷ 2 = 0  remainder 1  
        

  → Binary: 11001
• Fractional Part (0.375):
  Multiply by 2 repeatedly:

  0.375 × 2 = 0.75   → 0  
  0.75 × 2  = 1.5    → 1  
  0.5 × 2   = 1.0    → 1  
        

  → Binary: .011

✅ Final Binary Answer: (25.375)10 = (11001.011)2

Binary Division

Question: What is the quotient when 11010111 is divided by 101 in binary?

Step 1: Convert to decimal:

• 11010111 = 215
• 101 = 5

Step 2: Divide: 215 ÷ 5 = 43

Step 3: Convert 43 to binary = 101011

✅ Final Answer: 101011

Custom Number System: Position of 10A

Given digits: 0, 1, A (base-3)

Convert 10A to base-10:

• 1 → 1
• 0 → 0
• A → 2
• 10A = 1×9 + 0×3 + 2 = 11

List of numbers in sequence:

1. 00
2. 01
3. 0A
4. 10
5. 11
6. 1A
7. A0
8. A1
9. AA
10. 100
11. 101
12. 10A

✅ Final Answer: 12