The problem asks to find the hexadecimal equivalent of $X+Y$, where $X = 10010_2$ and $Y = 1111_2$ are binary numbers.

1. Problem Description

The problem asks to find the hexadecimal equivalent of $X+Y$, where $X = 10010_2$ and $Y = 1111_2$ are binary numbers.

2. Solution Steps

First, convert $X$ and $Y$ from binary to decimal.

$X = 10010_2 = 1 \cdot 2^4 + 0 \cdot 2^3 + 0 \cdot 2^2 + 1 \cdot 2^1 + 0 \cdot 2^0 = 16 + 2 = 18_{10}$.

$Y = 1111_2 = 1 \cdot 2^3 + 1 \cdot 2^2 + 1 \cdot 2^1 + 1 \cdot 2^0 = 8 + 4 + 2 + 1 = 15_{10}$.

Next, add $X$ and $Y$ in decimal:

$X + Y = 18 + 15 = 33_{10}$.

Now, convert the decimal result to hexadecimal. Divide 33 by 16:

$33 \div 16 = 2$ with a remainder of $1$.

So, $33_{10} = 2 \cdot 16^1 + 1 \cdot 16^0 = 21_{16}$.

3. Final Answer

The hexadecimal equivalent of X+Y is $21_{16}$.