2080 Baisakh · 1.5 marks

Convert (125.25)₁₀ to binary

Short answer

Divide 125 by 2 repeatedly: remainders give 1111101. Multiply 0.25 by 2: 0.5 (0), 1.0 (1) yields .01. Result: (1111101.01)₂.

Convert (125.25)₁₀ = (?)₂.

Integer: 125 → 62 r1, 31 r0, 15 r1, 7 r1, 3 r1, 1 r1, 0 r1 → read upwards: $1111101$ .

Fraction: 0.25 × 2 = 0.5 → 0; 0.5 × 2 = 1.0 → 1 → $.01$ .

Check: $64 + 32 + 16 + 8 + 4 + 1 + 0.25 = 125.25$ .

Answer: $(125.25)_{10} = (1111101.01)_2$

✓ Answer checked by Claude Opus 5.5 (high effort)

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