2075 Chaitra · 1.5 marks

Convert (53.125)₁₀ to binary

Short answer

Integer 53 by repeated division gives 110101; fractional 0.125 by repeated multiplication gives 0.001. Thus (53.125)₁₀ = (110101.001)₂.

Convert (53.125)₁₀ = (?)₂.

Convert the integer part by repeated division by 2 and the fraction part by repeated multiplication by 2.

Integer part (53):

Division	Quotient	Remainder
53 ÷ 2	26	1
26 ÷ 2	13	0
13 ÷ 2	6	1
6 ÷ 2	3	0
3 ÷ 2	1	1
1 ÷ 2	0	1

Bottom to top: $53_{10} = 110101_2$ .

Fraction part (0.125):

Multiplication	Result	Bit
0.125 × 2	0.25	0
0.25 × 2	0.5	0
0.5 × 2	1.0	1

Top to bottom: $0.125_{10} = 0.001_2$ .

Answer: $(53.125)_{10} = (110101.001)_2$

✓ Answer checked by Claude Opus 5.5 (high effort)

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