1. The problem is to understand how the numbers 8 and 1000 relate in binary and decimal systems. 2. The number 8 in decimal is represented in binary as $1000$. 3. Binary is a base-2 number system using only digits 0 and 1, where each digit represents a power of 2. 4. To convert decimal 8 to binary, find powers of 2 that sum to 8: $8 = 2^3$, so binary is $1000$ (1 at $2^3$, 0 elsewhere). 5. The binary number $1000$ equals decimal 8, confirming the equivalence. 6. Therefore, the answer 8 in decimal is the same as 1000 in binary.