Number base conversion: convert the binary number 1010000₂ into its equivalent octal representation by grouping bits in sets of three (from the right).

Introduction / Context:Binary–octal conversion is efficient because 8 = 2^3, so every octal digit corresponds to exactly three binary bits. Grouping the binary string into triples from the least significant side (rightmost) yields a quick, error-resistant method to obtain the octal value without intermediate decimal conversion.

Given Data / Assumptions:

• Binary input: 1010000₂.
• We may pad leading zeros to complete a leftmost group of three bits.
• No sign bit is involved; this is an unsigned magnitude conversion.

Concept / Approach:Partition the binary sequence into 3-bit groups from right to left. Translate each group to its octal digit using the mapping 000→0, 001→1, 010→2, 011→3, 100→4, 101→5, 110→6, 111→7. Concatenate the resulting octal digits.

Step-by-Step Solution:Binary: 1 010 000 (visual grouping from right).Pad leading zeros if desired: 001 010 000.Map groups: 001→1, 010→2, 000→0.Combine digits: 120 in base 8.Answer: 120₈.

Verification / Alternative check:Convert to decimal as a check: 1010000₂ = 64 + 16 = 80. Now 120₈ = 164 + 28 + 0 = 64 + 16 = 80. Both match.

Why Other Options Are Wrong:119₈, 101₈, 111₈: do not evaluate to 80 in decimal.None of the above: incorrect because 120₈ is correct.

Common Pitfalls:Grouping from the left instead of the right; forgetting to pad leading zeros; misreading 3-bit groups when zeros occur.

Final Answer:120₈