QUESTION 29 Convert (25.51)₈ to Binary value
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QUESTION 29
Convert (25.51)₈ to Binary value
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Answer: A. (010101.101001)₂
To convert octal to binary, each octal digit converts to exactly 3 binary digits. The octal digits 2, 5, 5, 1 convert to 010, 101, 101, 001 respectively, giving (010101.101001)₂. The decimal point position is preserved between the integer and fractional parts.
Step-by-step Derivation:
Step-by-step octal to binary conversion:
Separate integer and fractional parts: 25.51₈
- Integer part: 25₈
- Fractional part: 51₈
Convert each octal digit to 3-bit binary:
- 2₈ = 010₂
- 5₈ = 101₂
- 5₈ = 101₂
- 1₈ = 001₂
Concatenate with decimal point:
- (010101.101001)₂
Verification (convert back to decimal to check):
- Integer: 010101₂ = 0×32 + 1×16 + 0×8 + 1×4 + 0×2 + 1×1 = 21₁₀
- Check: 25₈ = 2×8 + 5×1 = 21₁₀ ✓
- Fractional: 101001₂ = 1×(1/2) + 0×(1/4) + 1×(1/8) + 0×(1/16) + 0×(1/32) + 1×(1/64) = 0.640625₁₀
- Check: 51₈ = 5×(1/8) + 1×(1/64) = 0.640625₁₀ ✓