To convert the hexadecimal number ( \text{FABCD1E}_{16} ) to octal, we can first convert it to binary and then group the binary digits into sets of three (since each octal digit represents three binary digits).
Then, we can convert each group of three binary digits to its octal equivalent.
Step 1: Convert Hexadecimal to Binary
[
\begin{align} \text{F} & : 1111 \ \text{A} & : 1010 \ \text{B} & : 1011 \ \text{C} & : 1100 \ \text{D} & : 1101 \ 1 & : 0001 \ E & : 1110 \ \end{align}
]
Concatenating these binary equivalents, we get ( \text{FABCD1E}_{16} ) as ( 11111010101111001101000111110_2 ).
Step 2: Group Binary Digits into Sets of Three
[ 111 \quad 110 \quad 101 \quad 011 \quad 110 \quad 011 \quad 010 \quad 001 \quad 111 \quad 10_2 ]
Step 3: Convert Binary Groups to Octal
[
\begin{align} 111 & : 7 \ 110 & : 6 \ 101 & : 5 \ 011 & : 3 \ 110 & : 6 \ 011 & : 3 \ 010 & : 2 \ 001 & : 1 \ 111 & : 7 \ 10 & : 2 \ \end{align}
]
Step 4: Concatenate Octal Digits
Concatenating these octal digits, we get ( 7653621712_{8} ).
So, ( \text{FABCD1E}{16} = 7653621712{8} ) after conversion from hexadecimal to octal.