Convert (25.51)₈ to Binary value

Each octal digit converts to exactly 3 binary bits: 2→010, 5→101, 5→101, 1→001. So (25.51)₈ = (010101.101001)₂. This is the standard octal-to-binary conversion where we replace each octal digit with its 3-bit binary equivalent.

Step-by-step Derivation:
Step 1: Convert octal integer part '25':

• 2 (octal) = 010 (binary)
• 5 (octal) = 101 (binary)
• Result: 010101 (binary)

Step 2: Convert octal fractional part '51':

• 5 (octal) = 101 (binary)
• 1 (octal) = 001 (binary)
• Result: 101001 (binary)

Step 3: Combine integer and fractional parts:

• (25.51)₈ = (010101.101001)₂

Verification:

• Integer: 0×2⁵ + 1×2⁴ + 0×2³ + 1×2² + 0×2¹ + 1×2⁰ = 16 + 4 + 1 = 21 (decimal) = 2×8¹ + 5×8⁰ ✓
• Fractional: 1×2⁻¹ + 0×2⁻² + 1×2⁻³ + 0×2⁻⁴ + 0×2⁻⁵ + 1×2⁻⁶ = 0.5 + 0.125 + 0.015625 = 0.640625 (decimal) = 5×8⁻¹ + 1×8⁻² ✓