Octal-to-binary conversion What is the correct binary representation of the octal number 45₈?

Introduction / Context:
Each octal digit maps to exactly three binary bits. Converting octal to binary is straightforward by replacing each digit with its 3-bit binary equivalent.

Given Data / Assumptions:

• Octal number: 45₈.
• Mapping: 0–7 → 000–111 in binary.

Concept / Approach:
Convert digit-by-digit: 4 → 100, 5 → 101. Concatenate in order: 100 101 → 100101.

Step-by-Step Solution:

Verification / Alternative check:
Convert 100101₂ back to octal by grouping in threes: 100 (4), 101 (5) → 45₈.

Why Other Options Are Wrong:

• 100010/100100/110101: Do not match the correct per-digit mapping.

Common Pitfalls:
Reversing digit order or using four bits per octal digit (incorrect).

Final Answer:
100101