In digital electronics, convert the following octal value to binary. What is the correct binary representation of 743₈ (octal 743)?

Introduction / Context:
Base conversion is a core skill in digital electronics. Octal (base 8) and binary (base 2) are closely related because each octal digit maps exactly to three binary bits. This question asks you to convert the octal number 743₈ into its binary equivalent without changing the numeric value, only the representation.

Given Data / Assumptions:

• Given number: 743 in base 8 (octal).
• Target: binary (base 2) representation.
• No arithmetic value change; only base conversion.

Concept / Approach:
Each octal digit corresponds to a 3-bit binary group: 0→000, 1→001, 2→010, 3→011, 4→100, 5→101, 6→110, 7→111. Therefore, convert each digit independently and then concatenate the groups from most significant to least significant. Leading zeros (if any) on the highest group may be omitted in the final binary string for compactness.

Step-by-Step Solution:
Map 7₈ → 111₂.Map 4₈ → 100₂.Map 3₂ → 011₂.Map 2₈ → 010₂.Concatenate: 111 100 011 010 → 111100011010₂.

Verification / Alternative check:
Alternative via decimal: 78^3 + 48^2 + 38 + 2 = 7512 + 4*64 + 24 + 2 = 3584 + 256 + 26 = 3866₁₀. Now convert 3866₁₀ to binary to confirm it is 111100011010₂. Both methods agree.

Why Other Options Are Wrong:
1111000110111₂ and 110011010111₂ change one or more 3-bit groups, altering the value. 111111111000₂ represents a different decimal value altogether. “None of the above” is incorrect because a correct mapping exists.

Common Pitfalls:
Mixing up the 3-bit group for 3 (011) or 4 (100); skipping a digit; forgetting that each octal digit always maps to exactly three binary bits.

Final Answer:
1111000110102