Decimal 100 converted to octal 144 using division by 8.

The image shows the process of converting a decimal number (100) into its octal (base-8) equivalent. Let's go through the solution step by step and verify it.

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🔢 Problem:

Convert the decimal number 100 to octal.

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✔ Method: Repeated Division by 8

To convert from decimal to octal, we repeatedly divide the number by 8 and keep track of the remainders. The octal number is formed by reading the remainders from bottom to top (reverse order).

Let’s perform the division:

#### Step 1: Divide 100 by 8
- 100 ÷ 8 = 12 remainder 4

#### Step 2: Divide 12 by 8
- 12 ÷ 8 = 1 remainder 4

#### Step 3: Divide 1 by 8
- 1 ÷ 8 = 0 remainder 1

Now, stop when the quotient becomes 0.

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📌 Collect the Remainders (from bottom to top):

- Last remainder: 1
- Then: 4
- Then: 4

So, reading the remainders in reverse order:
👉 1 4 4

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✔ Final Answer:

Octal of 100 (decimal) = 144₈

This matches the result shown in the image.

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🔍 Verification:

Let’s verify that 144₈ equals 100₁₀:

$$
1 \times 8^2 + 4 \times 8^1 + 4 \times 8^0 = 1 \times 64 + 4 \times 8 + 4 \times 1 = 64 + 32 + 4 = 100
$$

✔ Confirmed!

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✔ Conclusion:

The conversion is correct.

> Decimal 100 → Octal 144

The diagram correctly illustrates the process using repeated division by 8, collecting remainders, and reversing them to get the final octal number.

🟢 Answer: 144