The problem asks us to arrange the following numbers in ascending order: $57_8$, $2E_{16}$, $65$, $100011_2$.

1. Problem Description

The problem asks us to arrange the following numbers in ascending order: $57_8$, $2E_{16}$, $65$, $100011_2$.

2. Solution Steps

First, convert all the numbers to base

1

0. $57_8 = 5 \times 8^1 + 7 \times 8^0 = 5 \times 8 + 7 \times 1 = 40 + 7 = 47$

$2E_{16} = 2 \times 16^1 + E \times 16^0 = 2 \times 16 + 14 \times 1 = 32 + 14 = 46$

$65 = 65$

$100011_2 = 1 \times 2^5 + 0 \times 2^4 + 0 \times 2^3 + 0 \times 2^2 + 1 \times 2^1 + 1 \times 2^0 = 32 + 0 + 0 + 0 + 2 + 1 = 35$

Now we have the numbers in base 10 as: $47, 46, 65, 35$.

Arranging them in ascending order gives: $35, 46, 47, 65$.

Now, substitute the original numbers: $100011_2, 2E_{16}, 57_8, 65$.

3. Final Answer

$100011_2, 2E_{16}, 57_8, 65$