Solve the following math problem efficiently and clearly:

- For simple problems (2 steps or fewer):
Provide a concise solution with minimal explanation.

- For complex problems (3 steps or more):
Use this step-by-step format:

## Step 1: [Concise description]
[Brief explanation and calculations]

## Step 2: [Concise description]
[Brief explanation and calculations]

...

Regardless of the approach, always conclude with:

Therefore, the final answer is: $oxed{answer}$. I hope it is correct.

Where [answer] is just the final number or expression that solves the problem.

Problem: To transmit a positive integer less than 1000, the Networked Number Node offers two options.

Option 1. Pay $\$$d to send each digit d. Therefore, 987 would cost $\$$9 + $\$$8 + $\$$7 = $\$$24 to transmit.

Option 2. Encode integer into binary (base 2) first, and then pay $\$$d to send each digit d. Therefore, 987 becomes 1111011011 and would cost $\$$1 + $\$$1 + $\$$1 + $\$$1 + $\$$0 + $\$$1 + $\$$1 + $\$$0 + $\$$1 + $\$$1 = $\$$8.

What is the largest integer less than 1000 that costs the same whether using Option 1 or Option 2?
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