Introduction / Context:
Octal (base-8) numbers arise historically from grouping binary digits in sets of three. Converting octal to decimal reinforces positional-value understanding and prepares you for quick binary conversions as well.
Given Data / Assumptions:
- Octal input: 143₈.
- Octal digits range from 0 to 7.
- Place values: 8^0, 8^1, 8^2, ...
Concept / Approach:
- Use positional expansion: abc₈ = a8^2 + b8^1 + c8^0.
- Compute powers: 8^2 = 64, 8^1 = 8, 8^0 = 1.
Step-by-Step Solution:
143₈ = 18^2 + 48^1 + 38^0.Compute: 164 = 64; 48 = 32; 3*1 = 3.Sum: 64 + 32 + 3 = 99.
Verification / Alternative check:
Convert 143₈ → binary quickly: 1→001, 4→100, 3→011 giving 001 100 011₂ = 1100011₂ which equals 64 + 32 + 3 = 99₁₀.
Why Other Options Are Wrong:
- 90₁₀, 971₁₀, 107₁₀: Do not match the positional expansion result.
- None of the above: Incorrect because 99₁₀ is correct.
Common Pitfalls:
- Accidentally treating octal digits as decimal during expansion.
- Miscomputing 8^2 or 8^1, which skews the final sum.
Final Answer:
99₁₀
Discussion & Comments